JEE 2023 — Mathematics PYQ
JEE | Mathematics | 2023The number of the relations, on the set containing and , which are reflexive and transitive but not symmetric, is ___.
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The number of the relations, on the set containing and , which are reflexive and transitive but not symmetric, is ___.
Given that A = {1, 2, 3}
for reflexive, R must contain (1, 1), (2, 2), (3, 3)
for Transitive, (1, 2) & (2, 3) ∈ R then (1, 3) must be in
R for not symmetric (2, 1) & (3, 2) ∉R
As A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
Hence, there is only two possibilities of relations
which contain (3, 1) and not contain (3, 1).