# Proof by contradiction.

Printable View

• September 26th 2007, 09:07 AM
albee
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!!:)
• August 20th 2011, 04:14 PM
dgomes
Re: Proof by contradiction (please help, urgent) :)
Are you sure this expression is a contradiction? For me it is a tautology!
• August 20th 2011, 10:52 PM
terrorsquid
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.
• August 21st 2011, 11:54 AM
dgomes
Re: Proof by contradiction.
That is exactly what I found!