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## #1 2013-09-15 00:18:24

atran
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### Logical Equivalence and Logical Implication

Hi,

I read that two statements are logically equivalent if and only if they have the same truth value for every possible combination.
Does that mean the two statements are also semantically equivalent?

Are (A ⊢ B) and (P ≡ Q) statements/propositions?

Thanks for help.

## #2 2013-09-15 04:23:41

Nehushtan
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### Re: Logical Equivalence and Logical Implication

#### atran wrote:

Does that mean the two statements are also semantically equivalent?

Consider these two statements:

• I am married and I am happy.
• I am married but I am happy.

They are logically equivalent. Are they semantically equivalent as well?

## #3 2013-09-15 04:35:36

atran
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### Re: Logical Equivalence and Logical Implication

Hi,

What about (p⇒q ≡ ¬p∨q)? Why if two statements have the same truth values for every input, then the statements are also semantically the same?

Thanks.