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JEE Main20268 April 2026Evening ShiftMathematicsSets and RelationsActual

Consider the relation R on the set -2,-1,0,1,2 defined by (a, b) R if and only if 1+ab > 0 . Then, among the statements: I. The number of elements in R is 17 II. R is an equivalence relation

Options

  1. AOnly I is true
  2. BOnly II is true
  3. CBoth I and II are true
  4. DNeither I nor II is true

Correct answer

A. Only I is true

Step-by-step solution

The set is A = -2, -1, 0, 1, 2 . For Statement I, the relation is defined as (a, b) R 1 + ab > 0 . The pairs (a, b) that do not belong to R satisfy 1 + ab 0 ab -1 . The pairs satisfying ab -1 are (-2, 1), (-2, 2), (-1, 1), (-1, 2), (1, -2), (1, -1), (2, -2), (2, -1) . There are 8 such pairs. The total number of pairs in A A is 5 5 = 25 . The number of elements in R is 25 - 8 = 17 . Thus, Statement I is true. For Statement II, checking transitivity gives (-2, 0) R since 1 + (-2)(0) = 1 > 0 . Also, (0, 2) R since 1 +

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