# Math Help - Proof by contradiction.

1. ## Proof by contradiction.

Use Boolean algebra to show that ((p^q) implies (p implies q)) is a contradiction. do not use truth tables, thanks.
different question!!

Are you sure this expression is a contradiction? For me it is a tautology!

3. ## Re: Proof by contradiction.

I get a tautology too:

$((p\wedge q) \longrightarrow (p \longrightarrow q))$

$\equiv (-(p\wedge q)\vee (-p \vee q))$

$\equiv (-p\vee-q)\vee (-p\vee q)$

$\equiv -p\vee T$

$\equiv T$

Therefore it's a tautology.

4. ## Re: Proof by contradiction.

That is exactly what I found!