A and B are two sets. A has 10 members and B has 18 members. A ∪ B = 20 . The number of members in A ∩ B will be

This is a direct use of the inclusion-exclusion principle for two sets: n(A ∪ B) = n(A) + n(B) − n(A ∩ B). Here n(A) = 10, n(B) = 18 and n(A ∪ B) = 20. So 20 = 10 + 18 − n(A ∩ B), which gives n(A ∩ B) = 8. Option C is correct.

Why the others fail:

• A) 10: Substituting gives n(A ∪ B) = 18, not 20.
• B) 12: This gives n(A ∪ B) = 16, which contradicts the given union.
• D) 6: This gives n(A ∪ B) = 22, again not 20.

The core concept is set arithmetic with overlap, which is the same logic behind Venn diagram questions in CSAT and the classification of overlapping categories in census and survey tabulations. For Mains, it helps in reading data where one respondent can belong to two groups.

Trap: Many aspirants subtract the wrong quantity, such as computing 20 − 18 = 2 or 20 − 10 = 10, instead of subtracting the sum from the union. Always write the formula first and substitute.