If p = ducklings are fluffy , q = your feet smell , and r = math is awesome,and p is true and q and r are false, use the truth table in Ex. 79.1 todetermine the truth value of the converse of p→q.Select one:The converse is true.The converse is false.
Question
If p = ducklings are fluffy , q = your feet smell , and r = math is awesome,and p is true and q and r are false, use the truth table in Ex. 79.1 todetermine the truth value of the converse of p→q.Select one:The converse is true.The converse is false.
Solution
The statement p→q is "If ducklings are fluffy, then your feet smell." The converse of this statement is q→p, or "If your feet smell, then ducklings are fluffy."
Given that p is true (ducklings are fluffy) and q is false (your feet do not smell), we can determine the truth value of the converse.
In a truth table, the only time a conditional statement is false is when the first part is true and the second part is false. In this case, the first part of the converse (q) is false and the second part (p) is true. Therefore, the converse is true.
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