Simplifying a logical equivalence statement without a truth table

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needshelp5
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Homework Statement


[(p->r) ^ (q->r)] -> (p ^ q) -> r


Homework Equations


anything but a truth table! laws such as (p->q)= ~(p^~q) or (p->q)=(~q->~p) might help
 

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See how far you get using the relevant equations you showed. Other relevant equations that will come in handy are DeMorgan's Laws, ~(p ^ q) <==> ~p V ~q, and ~(p V q) <==> ~p ^ ~q.
 

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