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MathsMediumMCQ2023 · 31 Jan Shift 2

Q74.Among the relations S = {(a, b) : a, b ∈R −{0}, 2 + ab > 0} and T = {(a, b) : a, b ∈R, a2 −b2 ∈Z}, (1) S is transitive but T is not (2) both S and T are symmetric (3) neither S not T is transitive (4) T is symmetric but S is not ∈Z ∩[0, 4], 1 ≤i, j ≤2 . The number of matrices A such that the sum of all entries is a

What This Question Tests

The question asks to identify the properties (symmetric, transitive) of two given relations defined on real numbers, which requires applying the definitions and counterexamples where properties do not hold.

Concepts Tested

Symmetric relationTransitive relationDefinitions of relations on a set

Formulas Used

(a,b) in R => (b,a) in R (Symmetric)

(a,b) in R and (b,c) in R => (a,c) in R (Transitive)

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