Which of these statements is a tautology?

[MaryLaine]

I'm struggling with the concept of tautology. Could you please help me understand which of these statements are tautology and why?
> 1. (A⇒B) ⇒ (¬B⇒¬A)
> 2. (A⇒B) ⇒ (¬A⇒¬B)
> 3. (A⇒B) ⇒ (A∨B)
> 4. (A⇒B) ⇒ (B⇒A)

 

[lev888]

What is tautology? Can you give an example?

 

[pka]

I'm struggling with the concept of tautology. Could you please help me understand which of these statements are tautology and why?
> 1. (A⇒B) ⇒ (¬B⇒¬A)
> 2. (A⇒B) ⇒ (¬A⇒¬B)
> 3. (A⇒B) ⇒ (A∨B)
> 4. (A⇒B) ⇒ (B⇒A)

A tautology is a statement that is true for all truth values of its variables.
That is, looking at the truth table the final column is all T's.
Look at this example. The F tells us that is not a tautology.
However, look at this one Is that a tautology?