Simplifying a logical equivalence statement without a truth table

  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
  2. jcsd
  3. Mark44

    Staff: Mentor

    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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