# Math Help - A logic question

1. ## A logic question

Hello all.
Is the following expression true?
[ $( p \equiv q ) \wedge ( r \equiv s )$] $\Rightarrow$ [( $p \wedge r ) \equiv ( q \wedge s )$]
If yes, please prove it.

Thanks

2. ## Proof by Truth Table

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

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.