#### Answer

Neither the husband nor the wife watched television in $3$ of the $30$-day period.
Refer to the Venn Diagram below,

#### Work Step by Step

Draw two circles that overlap and label them (Husband, Wife).
The husband and wife watched television together for 18 days so write $18$ in the region where the circles overlap.
Since the husband watched television for a total of $20$ days, then it means that in $20-18=2$ of those days, he watched all by himself.
Since the wife watched television for a total of $25$ days, then it means that in $25-18=7$ of those days, she watched all by herself,
Write $2$ in the non-overlapping region inside the circle for Husband.
Write $7$ in the non-overlapping region inside the circle for Wife.
The two circles contain 18, 2, and 7.
Thus, either of them watched television for a total of $18+2+7=27$ days.
Therefore, in the given 30-day period, neither the husband nor the wife watched television for $30-17=3$ days.