What's the shortcut?

Logic Level 2

( A ⟺ B ) ⟺ ¬ ( A ⇒ B ) ⇒ ¬ ( B ⇒ A ) (A \iff B)\iff \neg (A \Rightarrow B)\Rightarrow \neg(B\Rightarrow A)

Two possible ways to prove if a statement is a tautology are these:
1. Build a truth table.
2. Supposing the statement is false and concluding a contradiction or not.

Is the mathematical statement at the top a tautology?

No, it isn't There's insufficient information Yes, it is

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Guillermo Templado by Guillermo Templado , 46, Spain

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2 solutions

V = T (Sorry, I'm Spanish, I forgot it)

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I don't get it. Isn't the statement false when A is false and B is true? I think you shoud check this case another time. Or may be I am just making a silly mistake.

Aiman Rafeed - 5 years, 5 months ago

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Please, check, (the implication is false) iff (the hypothesis is true and the conclusion is false)

Guillermo Templado - 5 years, 5 months ago

So what I'm gathering from this is that a is interchangeable with b. In the other equation it seems that a=b and then b=a. And those two equal the statement that a and b are interchangeable. I wish I could explain it better! Hope you understand what I'm trying to say!!

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