Exams › JEE Main › Maths
Consider the following statements:
Statement-1: If B = U A, then n(B) = n(U) − n(A), where U denotes the universal set.
Statement-2: For any three sets A, B and C, if C = A − B, then n(C) = n(A) − n(B).
Which of the following is correct?
- Statement-1 is true, and Statement-2 correctly explains Statement-1.
- Statement-1 is true, but Statement-2 does not correctly explain Statement-1.
- Statement-1 is false, while Statement-2 is true.
- Statement-1 is true, while Statement-2 is false.
Correct answer: Statement-1 is true, while Statement-2 is false.
Solution
If B is the complement of A then n(B) = n(U) - n(A), so Statement-1 is true. But for C = A - B, n(A-B) = n(A) - n(A intersect B), which equals n(A) - n(B) only when B is a subset of A; in general it is false. Hence Statement-1 true, Statement-2 false.
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