Question
Download Solution PDFConsider the following for any three non-empty sets A, B, and C
1. A – (B ∪ C) = (A - B) ∪ (A - C)
2. A – B = A – (A ∩ B)
3. A = (A ∩ B) ∪ (A - B)
Which of the above is/are correct?Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation:
Statement -1: A – (B ∪ C) = (A - B) ∪ (A - C)
LHS = (a, b, c, d) – (b, c, d, e, f, g) = a
RHS = (a, b) ∪ (a, d) = a, b, d
Here LHS ≠ RHS. So this statement is not correct.
Statement - 2: A – B = A – (A ∩ B)
LHS = a, b
RHS = (a, b, c, d) – (c, d) = a, b
So, this statement is correct.
Statement - 3: A = (A ∩ B) ∪ (A - B)
LHS = a, b, c, d
RHS = (c, d) ∪ (a, b) = a, b, c, d
So, this statement is also correct.
Hence, option (2) is correct.
Last updated on May 30, 2025
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