Discussion
How many villages were visited by both the salesmen ?
Answer: D
8 villages were visited by both salesmen.
Two of the 20 villages were visited by neither, so 18 were visited by at least one. By the inclusion-exclusion principle:
\[ \begin{aligned} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ 18 &= 14 + 12 - n(A \cap B) \\ n(A \cap B) &= 8 \end{aligned} \]
The option 26 simply adds 14 and 12, counting the shared villages twice; 6 is the number visited by A alone (14 - 8), and 4 the number visited by B alone (12 - 8).
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