4.6a Proofs

Matching. Drag sentences from the right to the correct location in the proof box. Don't print until you've come to the final page of this exercise.

First show that...

1. If two sentences are logically true in SL, then they are logically equivalent in SL.

P and Q are logically true sentences of SL.
by definition of logically true in SL, both P and Q are true on every truth value assignment.
there can be no truth value assignment making one of P and Q true and the other false. (None makes either false.)
by definition of equivalence, P and Q are logically equivalent in SL.
Suppose             __________
Then,          __________
So,          __________
So, finally,        __________