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NDA 1 2024 Maths, question 24

Topic: Algebra

Q24

For any three non-empty sets A,B,CA,B,C, what is (A∪B)−(A\cup B)- {(A−B)∪(B−A)∪(A∩B)(A-B)\cup (B-A)\cup (A\cap B)} equal to ?

  1. (a) Null setCorrect answer
  2. (b) AA
  3. (c) BB
  4. (d) (A∪B)−(A∩B)(A\cup B)-(A\cap B)

Solution.

Answer: (a) Null set

  1. The union A∪B is partitioned into A−B, B−A and A∩B.
  2. Their union is therefore A∪B itself.
  3. Removing it leaves the empty set; C is irrelevant to the expression.