# Math Help - Logical Equivalence

1. ## Logical Equivalence

I have trouble solving it.
Any help would be appreciated.

2. $[(p\lor q)\land (p\to r)\land (q\to r)]\to r$
=
$[(p\lor q)\land (\lnot p\lor r)\land (\lnot q\lor r)]\to r$
=
$\{(p\lor q)\land [(\lnot p\land \lnot q)\lor r]\}\to r$
=
$\{(p\lor q)\land [\lnot (p\lor q)\lor r]\}\to r$
=
$\{(p\lor q)\land [(p\lor q)\to r]\}\to r$

the last one is the tautology of modus ponens rule