# A logic question

• September 28th 2009, 07:21 AM
Researcher
A logic question
Hello all.
Is the following expression true?
[ $( p \equiv q ) \wedge ( r \equiv s )$] $\Rightarrow$ [( $p \wedge r ) \equiv ( q \wedge s )$]

Thanks
• September 29th 2009, 07:56 AM
Proof by Truth Table
Hello Researcher
Quote:

Originally Posted by Researcher
Hello all.
Is the following expression true?
[ $( p \equiv q ) \wedge ( r \equiv s )$] $\Rightarrow$ [( $p \wedge r ) \equiv ( q \wedge s )$]

Thanks

Yes - see the attached truth table for the proof.

The columns are evaluated in order from (1) to (7) - column (7) being the final result, which shows TRUE on every line.