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DISCRETE MATH: Determine if two statements are logically equivalent

  • Thread starter VinnyCee
  • Start date
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1. Homework Statement

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. Homework 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:rolleyes:
 

Answers and Replies

matt grime
Science Advisor
Homework Helper
9,394
3
Not very. Why not just write things out properly? As in for all z in S then P(z)
is just the same as z in S implies P(z).
 

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