Answer
If his wife does not cook and his child does not cook, then he does.
Work Step by Step
If he does not cook, his wife or child does.
Let p, q, and r represent the following simple statements:
p: He cooks.
q: His wife cooks.
r: His child cooks.
The given conditional statement can be represented in symbolic form as:
~p → (q v r)
An equivalent statement is the contrapositive:
~(q v r) → p
Using De-morgan's law, we find:
(~q ᴧ ~r) → p
If his wife does not cook and his child does not cook, then he does.
