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NDA 2 2024 Maths, question 35

Topic: Algebra

Q35

If AA and BB are two non-empty sets having 1010 elements in common, then how many elements do A×BA\times B and B×AB\times A have in common?

  1. (a) 1010
  2. (b) 2020
  3. (c) 4040
  4. (d) 100100Correct answer

Solution.

Answer: (d) 100100

  1. An ordered pair belongs to both A×B and B×A precisely when each coordinate belongs to A∩B.
  2. Their intersection is (A∩B)×(A∩B), containing 10×10=100 ordered pairs.