JEE 2023 — Mathematics PYQJEE | Mathematics | 2023Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation R = {(x, y) ∈ A × A : x + y =7} isChoose the correct answer:A. Symmetric but neither reflexive nor transitive (Correct Answer)B. Transitive but neither symmetric nor reflexiveC. An equivalence relationD. Reflexive but neither symmetric nor transitiveCorrect Answer: Symmetric but neither reflexive nor transitiveExplanationHere, A = {1, 2, 3, 4, 5, 6, 7} So, x + y = 7 => y = 7 - x ∴ R = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)} ∴ (a, b) ∈ R => (b, a) ∈ R ∴ R is symmetric only.ASymmetric but neither reflexive nor transitiveBTransitive but neither symmetric nor reflexiveCAn equivalence relationDReflexive but neither symmetric nor transitiveShow Answer SExplanationHere, A = {1, 2, 3, 4, 5, 6, 7} So, x + y = 7 => y = 7 - x ∴ R = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)} ∴ (a, b) ∈ R => (b, a) ∈ R ∴ R is symmetric only.
