UTpaper

Free mock tests & test series

Question 7Asked in UGC NET Computer Science, June 2016 (Paper II & III, Selected Questions)

Suppose that R₁ and R₂ are reflexive relations on a set A. Which of the following statements is correct?

  1. AR₁ ∩ R₂ is reflexive and R₁ ∪ R₂ is irreflexive.
  2. BR₁ ∩ R₂ is irreflexive and R₁ ∪ R₂ is reflexive.
  3. CBoth R₁ ∩ R₂ and R₁∪ R₂ are reflexive.
  4. DBoth R₁ ∩ R₂ and R₁ ∪ R₂ are irreflexive.
Show answerHide answer

Correct answer: (C) Both R₁ ∩ R₂ and R₁∪ R₂ are reflexive.

Explanation

If R₁ and R₂ are reflexive relations on a set A, then the diagonal Δ = {(a, a) : a ∈ A} is contained in both R₁ and R₂. R₁ ∪ R₂ is reflexive because Δ ⊆ R₁ ⊆ R₁ ∪ R₂. R₁ ∩ R₂ is also reflexive, because Δ ⊆ R₁ ∧ Δ ⊆ R₂ ⇒ Δ ⊆ R₁ ∩ R₂.

From UGC NET Computer Science PYQ, June 2016 (Paper II & III, Selected Questions)

This is question 7 of UGC NET Computer Science PYQ, June 2016 (Paper II & III, Selected Questions). See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.