(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Determine whether [tex]\forall\,x\,(P(x)\,\longleftrightarrow\,Q(x))[/tex] and [tex]\forall\,x\,P(x)\,\longleftrightarrow\,\forall\,x\,Q(x)[/tex] are logically equivalent. Justify your answer.

2. Relevant equations

[tex]P\,\longleftrightarrow\,Q[/tex] is only TRUE when both P and Q are TRUE or FALSE.

3. The attempt at a solution

No, I don't think the two statements are logically equivalent, but I have trouble trying to "justify" my answer.

Set P and Q as always TRUE.

Both statements are equivalent, but if you set P and Q to always FALSE, then the statements are no longer equivalent.

Does this seem logical

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# DISCRETE MATH: Determine if two statements are logically equivalent

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