#### 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.