Write the following two statements in symbolic form and determine whether they are logically equivalent. Include a truth table and a few words explaining how the truth table supports your answer.
If Sam is out of Schlitz, then Sam is out of beer.
Sam is not out of beer or Sam is not out of Schlitz.
The given statements are not logically equivalent. Let p be “Sam is out of Schlitz,” and q be “Sam is
out of beer.” Then the two statements have the following form:
p ? q and ? q? ? p:
The truth tables for these statement forms are
The table shows that p ? q and ? p? ? q sometimes have opposite truth values (shown in rows 1 and 2), and so p ? q ?? ? p? ? q:
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