Simplifying a logical equivalence statement without a truth table

by needshelp5
Tags: associativity, demorgan's law, logical equivalence
needshelp5 is offline
Jan25-10, 09:37 PM
P: 1
1. The problem statement, all variables and given/known data
[(p->r) ^ (q->r)] -> (p ^ q) -> r

2. Relevant equations
anything but a truth table! laws such as (p->q)= ~(p^~q) or (p->q)=(~q->~p) might help
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Mark44 is offline
Jan29-10, 03:50 PM
P: 21,012
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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