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NDA 2 2025 Maths, question 2

Topic: Algebra

Q2

If AA and BB are non-empty subsets of a set, and AcA^{c} and BcB^{c} represent their complements, then which of the following is/are correct?

I. A−B=Bc−AcA-B=B^{c}-A^{c}

II. A−Bc=Ac−BA-B^{c}=A^{c}-B

Select the answer using the code given below.

  1. (a) I onlyCorrect answer
  2. (b) II only
  3. (c) Both I and II
  4. (d) Neither I nor II

Solution.

Answer: (a) I only

  1. A − B = A ∩ Bᶜ, while Bᶜ − Aᶜ = Bᶜ ∩ A, so I is true.
  2. But A − Bᶜ = A ∩ B and Aᶜ − B = Aᶜ ∩ Bᶜ, which are not generally equal.
  3. For example, in U={1,2}, take A=B={1}: the latter sets are {1} and {2}.