Prove that:
(P -> (Q->R)) <-> ((R->Q)->P)
and
P^ ((~Q)v R) v (Q^(~R)) are logically equivalent.
I will put this in words:
Prove that:
If P imples Q which implies R and P implies R, then R and Q imply P and vice versa,
is logically equivalent with:
P and not Q or R or Q and not R are logically equivalent.
(P -> (Q->R)) <-> ((R->Q)->P)
and
P^ ((~Q)v R) v (Q^(~R)) are logically equivalent.
I will put this in words:
Prove that:
If P imples Q which implies R and P implies R, then R and Q imply P and vice versa,
is logically equivalent with:
P and not Q or R or Q and not R are logically equivalent.
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Use a truth table. It's sloppy, but it will give you the proof you need.