Let P(x) and Q(x) be arbitrary predicates. Which of the following statements is always TRUE?

A | ((∀x(P(x)∨Q(x))))⟹((∀xP(x))∨(∀xQ(x))) |

B | (∀x(P(x)⟹Q(x)))⟹((∀xP(x))⟹(∀xQ(x))) |

C | (∀x(P(x))⟹∀x(Q(x)))⟹(∀x(P(x)⟹Q(x))) |

D | (∀x(P(x))⇔(∀x(Q(x))))⟹(∀x(P(x)⇔Q(x))) |

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Let P(x) and Q(x) be arbitrary predicates. Which of the following statements is always TRUE?

A | ((∀x(P(x)∨Q(x))))⟹((∀xP(x))∨(∀xQ(x))) |

B | (∀x(P(x)⟹Q(x)))⟹((∀xP(x))⟹(∀xQ(x))) |

C | (∀x(P(x))⟹∀x(Q(x)))⟹(∀x(P(x)⟹Q(x))) |

D | (∀x(P(x))⇔(∀x(Q(x))))⟹(∀x(P(x)⇔Q(x))) |

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