GATE FORUM - Recent questions and answers in Mathematics
http://gateforum.org//qa/mathematics
Powered by Question2AnswerAnswered: NOT necessarily a property of a Group
http://gateforum.org//1729/not-necessarily-a-property-of-a-group?show=2411#a2411
<table style="width:741px"><tbody><tr><td style="vertical-align:top"><p>A</p></td><td style="vertical-align:top"><p>Commutativity</p></td></tr></tbody></table>Set Theory & Algebrahttp://gateforum.org//1729/not-necessarily-a-property-of-a-group?show=2411#a2411Tue, 22 Aug 2017 12:26:58 +0000Answered: The minimum number of colours that is sufficient to vertex-colour any planar graph
http://gateforum.org//1703/the-minimum-number-of-colours-that-is-sufficient-to-vertex-colour-any-planar-graph?show=2407#a2407
<p><span style="color:rgb(0, 0, 0); font-family:open sans,sans-serif; font-size:15px">If we talk about minimum no. of colors that is sufficient to vertex-color in any planar graph which means a planar graph with any no. of vertices. However, in some cases, 3 colors are suffcient to vertex-color in a planar graph like triangle whereas in some cases 4 colors are suffcient to vertex-color in a planar graph . But is has been proved that 4 colors are sufficient to vertex-color every planar graph. It is called as the four color theorem. So, the answer will be 4.</span></p>Graphshttp://gateforum.org//1703/the-minimum-number-of-colours-that-is-sufficient-to-vertex-colour-any-planar-graph?show=2407#a2407Fri, 16 Jun 2017 02:36:44 +0000Answered: Which of the following statements is always TRUE
http://gateforum.org//1675/which-of-the-following-statements-is-always-true?show=2406#a2406
A ((∀x(P(x)∨Q(x))))⟹((∀xP(x))∨(∀xQ(x)))Propositional and first order logichttp://gateforum.org//1675/which-of-the-following-statements-is-always-true?show=2406#a2406Sat, 10 Jun 2017 09:05:29 +0000Answered: bisection method is applied to compute a zero of the function
http://gateforum.org//1706/bisection-method-is-applied-to-compute-a-zero-of-the-function?show=2404#a2404
At 3rd iteration the value of function becomes zero that is at x3=2Numerical Methodshttp://gateforum.org//1706/bisection-method-is-applied-to-compute-a-zero-of-the-function?show=2404#a2404Mon, 29 May 2017 13:44:11 +0000Answered: Newton-Raphson method is used to compute a root of the equation
http://gateforum.org//1707/newton-raphson-method-is-used-to-compute-a-root-of-the-equation?show=2355#a2355
3.607142 is the answerNumerical Methodshttp://gateforum.org//1707/newton-raphson-method-is-used-to-compute-a-root-of-the-equation?show=2355#a2355Sun, 08 Jan 2017 12:39:05 +0000Answered: trapezoidal method is used to evaluate the integral obtained
http://gateforum.org//1713/trapezoidal-method-is-used-to-evaluate-the-integral-obtained?show=2354#a2354
c . is always = 1/3Numerical Methodshttp://gateforum.org//1713/trapezoidal-method-is-used-to-evaluate-the-integral-obtained?show=2354#a2354Sun, 08 Jan 2017 12:34:30 +0000Need writing help for statistics essays?
http://gateforum.org//2350/need-writing-help-for-statistics-essays
<p>I am a graduate student I am studying B.sc math’s and sometimes I have to write essay as our writing task. Today I got essay writing task on statistics. I am not good in writing works. I want to submit good quality content, sample papers, and essay models for my writing task I think I can’t even use my friend’s paper to copy. Therefore I need some tips abd may i use <strong><a rel="nofollow" href="http://rospher.com">custom essay writing service</a></strong> to complete this statistics essay introduction. So kindly help me start this essay easily and complete before the deadline. Your small support is very useful for me so please share your tips.</p>Mathematicshttp://gateforum.org//2350/need-writing-help-for-statistics-essaysThu, 22 Dec 2016 04:23:51 +0000Answered: probability that the face value exceeds
http://gateforum.org//1628/probability-that-the-face-value-exceeds?show=2306#a2306
<p>Ans, 0.468</p><p></p><p>Let P<sub>n </sub>be the probability of corresponding face value occurence.</p><p>Total probability</p><p>P<sub>1</sub> + P<sub>2</sub> + P<span style="font-size:10.8333px; line-height:17.3333px">3</span> + P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> = 1 .......... Eq. 1</p><p>According to conditions,</p><p>P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 0.9( P<sub>2 </sub>+ P<sub>4</sub> + P<sub>6 </sub>) ............... Eq. 2</p><p>P<sub>4</sub> + P<sub>6 </sub>= 0.75( P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> ) ..................... Eq. 3</p><p>but P<sub>2 </sub>= P<sub>4</sub> = P<sub>6 </sub>= P given</p><p>So Eq, 1 P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 1 - 3P<sub>2</sub></p><p>Eq. 2 P<sub>1</sub> + P<span style="font-size:10.8333px">3</span> + P<sub>5 </sub>= 0.9 * 3P<sub>2</sub></p><p>Soving these, P<sub>2 </sub>= P<sub>4</sub> = P<sub>6 </sub>= P = 0.1754</p><p>Putting it in Eq. 3 P<sub>4</sub> + P<sub>5</sub> + P<sub>6</sub> = 0.468</p><p></p>Probabilityhttp://gateforum.org//1628/probability-that-the-face-value-exceeds?show=2306#a2306Wed, 10 Aug 2016 12:19:44 +0000Answered: Consider the binary relation reflexive transitive closure
http://gateforum.org//1739/consider-the-binary-relation-reflexive-transitive-closure?show=1740#a1740
<table><tbody><tr><td><p>{(x, y) | y ≥ x and x, y ∈ {0, 1, 2, ... }}</p></td></tr></tbody></table>Set Theory & Algebrahttp://gateforum.org//1739/consider-the-binary-relation-reflexive-transitive-closure?show=1740#a1740Sat, 20 Feb 2016 22:08:50 +0000Answered: equivalence relations on a non-empty set
http://gateforum.org//1737/equivalence-relations-on-a-non-empty-set?show=1738#a1738
<table><tbody><tr><td><p>R ∩ S is an equivalence relation</p></td></tr></tbody></table>Set Theory & Algebrahttp://gateforum.org//1737/equivalence-relations-on-a-non-empty-set?show=1738#a1738Sat, 20 Feb 2016 22:08:06 +0000Answered: relation R is defined on ordered pairs of integers as follows
http://gateforum.org//1735/relation-r-is-defined-on-ordered-pairs-of-integers-as-follows?show=1736#a1736
Neither a Partial Order nor an Equivalence RelationSet Theory & Algebrahttp://gateforum.org//1735/relation-r-is-defined-on-ordered-pairs-of-integers-as-follows?show=1736#a1736Sat, 20 Feb 2016 22:06:32 +0000Answered: number of ordered pairs in the largest and the smallest equivalence relations
http://gateforum.org//1733/number-of-ordered-pairs-in-the-largest-and-the-smallest-equivalence-relations?show=1734#a1734
<p>B</p><p>n<sup>2</sup> and n</p>Set Theory & Algebrahttp://gateforum.org//1733/number-of-ordered-pairs-in-the-largest-and-the-smallest-equivalence-relations?show=1734#a1734Sat, 20 Feb 2016 22:05:42 +0000Answered: binary relation R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE
http://gateforum.org//1731/binary-relation-r-x-y-x-z-z-x-z-y-on-the-set-x-y-z-which-one-of-the-following-is-true?show=1732#a1732
<table><tbody><tr><td><p>R is neither symmetric nor antisymmetric</p></td></tr></tbody></table>Set Theory & Algebrahttp://gateforum.org//1731/binary-relation-r-x-y-x-z-z-x-z-y-on-the-set-x-y-z-which-one-of-the-following-is-true?show=1732#a1732Sat, 20 Feb 2016 22:05:03 +0000multiplication operation, the structure (S, *) forms A
http://gateforum.org//1728/multiplication-operation-the-structure-s-forms-a
<p>Consider the set S = {1, ω, ω2}, where ω and w<sup>2</sup> are cube roots of unity. If * denotes the multiplication operation, the structure (S, *) forms</p><table><tbody><tr><td><p>A</p></td><td><p>A group</p></td></tr><tr><td><p>B</p></td><td><p>A ring</p></td></tr><tr><td><p>C</p></td><td><p>An integral domain</p></td></tr><tr><td><p>D</p></td><td><p>A field</p></td></tr></tbody></table>Set Theory & Algebrahttp://gateforum.org//1728/multiplication-operation-the-structure-s-forms-aSat, 20 Feb 2016 22:03:49 +0000Answered: Suppose that the eigenvalues of matrix A are 1, 2, 4. The determinant
http://gateforum.org//1726/suppose-that-the-eigenvalues-of-matrix-a-are-1-2-4-the-determinant?show=1727#a1727
Determinant of A = 1*4*2 = 8 which is product of Eigen values. Determinant of A-1 = 1/8 as determinant of inverse of matrix is inverse of determinant. Determinant of Transpose (A-1) = 1/8Linear Algebrahttp://gateforum.org//1726/suppose-that-the-eigenvalues-of-matrix-a-are-1-2-4-the-determinant?show=1727#a1727Sat, 20 Feb 2016 22:02:58 +0000Answered: each consisting of m linear equations in n variables
http://gateforum.org//1724/each-consisting-of-m-linear-equations-in-n-variables?show=1725#a1725
<table><tbody><tr><td><p>Only III is true</p></td></tr></tbody></table>Linear Algebrahttp://gateforum.org//1724/each-consisting-of-m-linear-equations-in-n-variables?show=1725#a1725Sat, 20 Feb 2016 22:02:09 +0000f (x) be a polynomial and g(x) = f (x) be its derivative. If the degree
http://gateforum.org//1723/f-x-be-a-polynomial-and-g-x-f-x-be-its-derivative-if-the-degree
Let f (x) be a polynomial and g(x) = f (x) be its derivative. If the degree of (f(x) + f(−x)) is 10, then the degree of (g(x) − g(−x)) is _______________Linear Algebrahttp://gateforum.org//1723/f-x-be-a-polynomial-and-g-x-f-x-be-its-derivative-if-the-degreeSat, 20 Feb 2016 22:01:26 +0000Answered: following system has non-trivial solution
http://gateforum.org//1721/following-system-has-non-trivial-solution?show=1722#a1722
|A| should be 0 for non-trivial solution.Linear Algebrahttp://gateforum.org//1721/following-system-has-non-trivial-solution?show=1722#a1722Sat, 20 Feb 2016 22:00:56 +0000Answered: Perform the following operations on the matrix
http://gateforum.org//1719/perform-the-following-operations-on-the-matrix?show=1720#a1720
0<br />
<br />
last column is a multiple of first column. If we multiply 15 with first column, we get the third column.Linear Algebrahttp://gateforum.org//1719/perform-the-following-operations-on-the-matrix?show=1720#a1720Sat, 20 Feb 2016 22:00:20 +0000larger of the two eigenvalues of the matrix
http://gateforum.org//1718/larger-of-the-two-eigenvalues-of-the-matrix
<p>The larger of the two eigenvalues of the matrix</p><pre>⎡ 4 5 ⎤
⎣ 2 1 ⎦</pre><p>is ____</p>Linear Algebrahttp://gateforum.org//1718/larger-of-the-two-eigenvalues-of-the-matrixSat, 20 Feb 2016 21:59:14 +0000Which of the following statements is correct
http://gateforum.org//1717/which-of-the-following-statements-is-correct
<p>Consider the following statements:</p><pre>S1: The sum of two singular n × n matrices may be non-singular
S2: The sum of two n × n non-singular matrices may be singular. </pre><p>Which of the following statements is correct?</p><table><tbody><tr><td><p>A</p></td><td><p>S1 and S2 are both true</p></td></tr><tr><td><p>B</p></td><td><p>S1 is true, S2 is false</p></td></tr><tr><td><p>C</p></td><td><p>S1 is false, S2 is true</p></td></tr><tr><td><p>D</p></td><td><p>S1 and S2 are both false</p></td></tr></tbody></table>Linear Algebrahttp://gateforum.org//1717/which-of-the-following-statements-is-correctSat, 20 Feb 2016 21:58:42 +0000How many solutions does the following system of linear equations have
http://gateforum.org//1716/how-many-solutions-does-the-following-system-of-linear-equations-have
<p>How many solutions does the following system of linear equations have ?</p><pre> -x + 5y = -1
x - y = 2
x + 3y = 3</pre><table><tbody><tr><td><p>A</p></td><td><p>infinitely many</p></td></tr><tr><td><p>B</p></td><td><p>two distinct solutions</p></td></tr><tr><td><p>C</p></td><td><p>unique</p></td></tr><tr><td><p>D</p></td><td><p>none of these</p></td></tr></tbody></table>Linear Algebrahttp://gateforum.org//1716/how-many-solutions-does-the-following-system-of-linear-equations-haveSat, 20 Feb 2016 21:58:07 +0000Which one of the following statements is TRUE
http://gateforum.org//1715/which-one-of-the-following-statements-is-true
<p>Which one of the following statements is TRUE about every</p><table><tbody><tr><td><p>A</p></td><td><p>If the trace of the matrix is positive and the determinant of the matrix is negative, at least one of its eigenvalues is negative.</p></td></tr><tr><td><p>B</p></td><td><p>If the trace of the matrix is positive, all its eigenvalues are positive.</p></td></tr><tr><td><p>C</p></td><td><p>If the determinant of the matrix is positive, all its eigenvalues are positive.</p></td></tr><tr><td><p>D</p></td><td><p>If the product of the trace and determinant of the matrix is positive, all its eigenvalues are positive.</p></td></tr></tbody></table>Linear Algebrahttp://gateforum.org//1715/which-one-of-the-following-statements-is-trueSat, 20 Feb 2016 21:57:12 +0000product of the non-zero eigenvalues of the matrix
http://gateforum.org//1714/product-of-the-non-zero-eigenvalues-of-the-matrix
<p>The product of the non-zero eigenvalues of the matrix</p><pre>1 0 0 0 1
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
1 0 0 0 1</pre><p>is ______</p>Linear Algebrahttp://gateforum.org//1714/product-of-the-non-zero-eigenvalues-of-the-matrixSat, 20 Feb 2016 21:56:41 +0000Newton-Raphson method
http://gateforum.org//1712/newton-raphson-method
<p>In the Newton-Raphson method, an initial guess of x0 = 2 is made and the sequence x0, x1, x2 … is obtained for the function</p><p><strong>0.75x<sup>3</sup> – 2x<sup>2</sup> – 2x + 4 = 0 Consider the statements<br>(I) x<sub>3</sub> = 0.<br>(II) The method converges to a solution in a finite number of iterations.</strong></p><p>Which of the following is TRUE?</p><table><tbody><tr><td><p>A</p></td><td><p>Only I</p></td></tr><tr><td><p>B</p></td><td><p>Only II</p></td></tr><tr><td><p>C</p></td><td><p>Both I and II</p></td></tr><tr><td><p>D</p></td><td><p>Neither I nor II</p></td></tr></tbody></table>Numerical Methodshttp://gateforum.org//1712/newton-raphson-methodSat, 20 Feb 2016 21:53:15 +0000Answered: continuous for all real values
http://gateforum.org//1710/continuous-for-all-real-values?show=1711#a1711
P is true and Q is falseCalculushttp://gateforum.org//1710/continuous-for-all-real-values?show=1711#a1711Sat, 20 Feb 2016 21:52:10 +0000curve is said to be an extremum if it is a local minimum or a local maximum
http://gateforum.org//1709/curve-is-said-to-be-an-extremum-if-it-is-a-local-minimum-or-a-local-maximum
<p>A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x<sup>4</sup> - 16x<sup>3</sup> + 24x<sup>2</sup> + 37</p>Calculushttp://gateforum.org//1709/curve-is-said-to-be-an-extremum-if-it-is-a-local-minimum-or-a-local-maximumSat, 20 Feb 2016 21:51:23 +0000Answered: number and location(s) of the local minima of this function
http://gateforum.org//1704/number-and-location-s-of-the-local-minima-of-this-function?show=1705#a1705
<table><tbody><tr><td><p>Two, at π/4 and 3π/2</p></td></tr></tbody></table>Calculushttp://gateforum.org//1704/number-and-location-s-of-the-local-minima-of-this-function?show=1705#a1705Sat, 20 Feb 2016 21:48:43 +0000connected graph, a bridge is an edge whose removal disconnects a graph
http://gateforum.org//1702/connected-graph-a-bridge-is-an-edge-whose-removal-disconnects-a-graph
<p>In a connected graph, a bridge is an edge whose removal disconnects a graph. Which one of the following statements is True?</p><table><tbody><tr><td><p>A</p></td><td><p>A tree has no bridge</p></td></tr><tr><td><p>B</p></td><td><p>A bridge cannot be part of a simple cycle</p></td></tr><tr><td><p>C</p></td><td><p>Every edge of a clique with size ≥ 3 is a bridge (A clique is any complete subgraph of a graph)</p></td></tr><tr><td><p>D</p></td><td><p>A graph with bridges cannot have a cycle</p></td></tr></tbody></table>Graphshttp://gateforum.org//1702/connected-graph-a-bridge-is-an-edge-whose-removal-disconnects-a-graphSat, 20 Feb 2016 21:46:43 +0000perfect matchings are there in a complete graph
http://gateforum.org//1701/perfect-matchings-are-there-in-a-complete-graph
How many perfect matchings are there in a complete graph of 6 vertices ?Graphshttp://gateforum.org//1701/perfect-matchings-are-there-in-a-complete-graphSat, 20 Feb 2016 21:46:12 +0000number of faces in the planar embedding of the graph is
http://gateforum.org//1700/number-of-faces-in-the-planar-embedding-of-the-graph-is
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph isGraphshttp://gateforum.org//1700/number-of-faces-in-the-planar-embedding-of-the-graph-isSat, 20 Feb 2016 21:45:29 +0000cycle on n vertices is isomorphic to its complement
http://gateforum.org//1699/cycle-on-n-vertices-is-isomorphic-to-its-complement
A cycle on n vertices is isomorphic to its complement. The value of n is _____.Graphshttp://gateforum.org//1699/cycle-on-n-vertices-is-isomorphic-to-its-complementSat, 20 Feb 2016 21:44:58 +0000Answered: number of edges in a bipartite graph
http://gateforum.org//1697/number-of-edges-in-a-bipartite-graph?show=1698#a1698
Number of edges would be maximum when there are 6 edges on each side and every vertex is connected to all 6 vertices of the other side.Graphshttp://gateforum.org//1697/number-of-edges-in-a-bipartite-graph?show=1698#a1698Sat, 20 Feb 2016 21:44:27 +0000Answered: graphs has an Eulerian circuit
http://gateforum.org//1695/graphs-has-an-eulerian-circuit?show=1696#a1696
<table><tbody><tr><td><p>The complement of a cycle on 25 vertices</p></td></tr></tbody></table>Graphshttp://gateforum.org//1695/graphs-has-an-eulerian-circuit?show=1696#a1696Sat, 20 Feb 2016 21:43:49 +0000Answered: non-planar graph with the minimum possible number of edges
http://gateforum.org//1693/non-planar-graph-with-the-minimum-possible-number-of-edges?show=1694#a1694
<table><tbody><tr><td><p>9 edges and 6 vertices</p></td></tr></tbody></table>Graphshttp://gateforum.org//1693/non-planar-graph-with-the-minimum-possible-number-of-edges?show=1694#a1694Sat, 20 Feb 2016 21:43:17 +0000Answered: partitioned into two edge-disjoint spanning trees
http://gateforum.org//1691/partitioned-into-two-edge-disjoint-spanning-trees?show=1692#a1692
There are two vertex-disjoint paths between every pair of verticesGraphshttp://gateforum.org//1691/partitioned-into-two-edge-disjoint-spanning-trees?show=1692#a1692Sat, 20 Feb 2016 21:42:47 +0000Answered: true for every planar graph on n vertices
http://gateforum.org//1689/true-for-every-planar-graph-on-n-vertices?show=1690#a1690
The graph has a vertex-cover of size at most 3n/4Graphshttp://gateforum.org//1689/true-for-every-planar-graph-on-n-vertices?show=1690#a1690Sat, 20 Feb 2016 21:42:10 +0000sequences can not be the degree sequence of any graph
http://gateforum.org//1688/sequences-can-not-be-the-degree-sequence-of-any-graph
<p>The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph?</p><pre>I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1 </pre>Graphshttp://gateforum.org//1688/sequences-can-not-be-the-degree-sequence-of-any-graphSat, 20 Feb 2016 21:41:25 +0000Answered: number of bounded faces in any embedding of G on the plane is equal to
http://gateforum.org//1686/number-of-bounded-faces-in-any-embedding-of-g-on-the-plane-is-equal-to?show=1687#a1687
<pre>10 - 15 + f = 2
f = 7
There is always one unbounded face, so the number of bounded faces = 6</pre>Graphshttp://gateforum.org//1686/number-of-bounded-faces-in-any-embedding-of-g-on-the-plane-is-equal-to?show=1687#a1687Sat, 20 Feb 2016 21:40:42 +0000Answered: line graph of a clique is a clique
http://gateforum.org//1684/line-graph-of-a-clique-is-a-clique?show=1685#a1685
<pre> The line graph of a cycle is a cycle.</pre>Graphshttp://gateforum.org//1684/line-graph-of-a-clique-is-a-clique?show=1685#a1685Sat, 20 Feb 2016 21:40:01 +0000Answered: Sum of degrees of all vertices is even
http://gateforum.org//1682/sum-of-degrees-of-all-vertices-is-even?show=1683#a1683
Both P and QGraphshttp://gateforum.org//1682/sum-of-degrees-of-all-vertices-is-even?show=1683#a1683Sat, 20 Feb 2016 21:39:20 +0000How many 4-digit even numbers have all 4 digits distinct?
http://gateforum.org//1681/how-many-4-digit-even-numbers-have-all-4-digits-distinct
Combinatoricshttp://gateforum.org//1681/how-many-4-digit-even-numbers-have-all-4-digits-distinctSat, 20 Feb 2016 21:37:03 +0000colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of k colours
http://gateforum.org//1680/colouring-book-which-each-english-letter-drawn-times-wants-paint-each-these-prints-with-colours
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of k colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of k that satisfies this requirement ?Combinatoricshttp://gateforum.org//1680/colouring-book-which-each-english-letter-drawn-times-wants-paint-each-these-prints-with-coloursSat, 20 Feb 2016 21:36:14 +0000number of reflexive relations on a set of 5 elements
http://gateforum.org//1679/number-of-reflexive-relations-on-a-set-of-5-elements
What is the possible number of reflexive relations on a set of 5 elements?Combinatoricshttp://gateforum.org//1679/number-of-reflexive-relations-on-a-set-of-5-elementsSat, 20 Feb 2016 21:35:30 +0000Answered: How many onto (or surjective) functions are there from an n-element
http://gateforum.org//1677/how-many-onto-or-surjective-functions-are-there-from-an-n-element?show=1678#a1678
<p>total number of onto functions is 2<sup>n</sup> - 2</p>Combinatoricshttp://gateforum.org//1677/how-many-onto-or-surjective-functions-are-there-from-an-n-element?show=1678#a1678Sat, 20 Feb 2016 21:35:08 +0000Answered: sound inference rules of logic
http://gateforum.org//1673/sound-inference-rules-of-logic?show=1674#a1674
If a person is kind, he is not known to be corruptPropositional and first order logichttp://gateforum.org//1673/sound-inference-rules-of-logic?show=1674#a1674Sat, 20 Feb 2016 21:31:25 +0000Answered: propositional statement is (P → (Q v R)) → ((P ^ Q) → R)
http://gateforum.org//1671/propositional-statement-is-p-%E2%86%92-q-v-r-%E2%86%92-p-q-%E2%86%92-r?show=1672#a1672
<table><tbody><tr><td><p>satisfiable but not valid</p></td></tr></tbody></table>Propositional and first order logichttp://gateforum.org//1671/propositional-statement-is-p-%E2%86%92-q-v-r-%E2%86%92-p-q-%E2%86%92-r?show=1672#a1672Sat, 20 Feb 2016 21:30:10 +0000Answered: correct translation into logical notation of the following assertion
http://gateforum.org//1669/correct-translation-into-logical-notation-of-the-following-assertion?show=1670#a1670
(∃x) (boy(x) ∧ (∀y) (girl(y) → taller(x,y)))Propositional and first order logichttp://gateforum.org//1669/correct-translation-into-logical-notation-of-the-following-assertion?show=1670#a1670Sat, 20 Feb 2016 21:29:40 +0000Answered: Every teacher is liked by some student
http://gateforum.org//1667/every-teacher-is-liked-by-some-student?show=1668#a1668
<table><tbody><tr><td><p>∀ (x) [teacher (x) → ∃ (y) [student (y) ^ likes (y, x)]]</p></td></tr></tbody></table>Propositional and first order logichttp://gateforum.org//1667/every-teacher-is-liked-by-some-student?show=1668#a1668Sat, 20 Feb 2016 21:29:01 +0000Answered: atomic prepositional assertions
http://gateforum.org//1665/atomic-prepositional-assertions?show=1666#a1666
<pre>Answer : [ B ]</pre>Propositional and first order logichttp://gateforum.org//1665/atomic-prepositional-assertions?show=1666#a1666Sat, 20 Feb 2016 21:28:22 +0000