Consider the following statements:
S : ∀xP(x) ∨ ∀xQ(x) 1 and ∀x(P(x) ∨ Q(x)) are not logically equivalent.
S : ∃xP(x) ∧ ∃xQ(x) 2 and ∃x(P(x) ∧ Q(x)) are not logically equivalent Which of the following statements is/are correct?
Pick an option to check yourself, or open the answer below.
Show answer & explanation
Correct answer: C. Both 1 and 2 S S
Explanation
∀xP ∨ ∀xQ implies ∀x(P ∨ Q) but not conversely, and ∃x(P ∧ Q) implies ∃xP ∧ ∃xQ but not conversely. Both pairs are not equivalent, so both statements are correct.
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