JEE Main 2024 Mathematics question

Mathematics Sets and Relation JEE Main 2024

Let A = {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15}. Let R be a relation on A × B define by (a, b) R (c, d) if and only if 3ad − 7bc is an even integer. Then the relation R is:

(A)reflexive but not symmetric.
(B)transitive but not symmetric.
(C)reflexive and symmetric but not transitive.Correct
(D)an equivalence relation.

Answer: (C)

Solution

3ad − 7bc is even iff ad + bc is even. It holds for (a, b) R (a, b) since 2ab is even (reflexive), and the condition is symmetric in the two pairs

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-012465