JEE 2024 — Mathematics PYQ

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Question

JEE 2024 — Mathematics PYQ

JEE | Mathematics | 2024

If R is the smallest equivalence relation on the set {1, 2, 3, 4} such that {(1, 2), (1, 3)}
⊂ R, then the number of elements in R is ................. .

Choose the correct answer:

Explanation

A = {1, 2, 3, 4}
R = {(1, 2) (1, 3)}
for reflexive we need to have = (1, 1), (2, 2), (3, 3), (4, 4)
For symmetric
(1, 2) Î R Þ (2, 1) Î R
(1, 3) Î R Þ (3, 1) Î R
R becomes
{(1, 1) (2, 2) (3, 3) (4, 4) (1, 2) (2, 1), (1, 3), (3, 1)}
Now (3, 1) & (1, 2) both belongs to R
So for transitive (3, 2) must be on R
(3, 2) must be added
again for symmetric (2, 3) also be an element
R = {(1, 1) (2, 2) (3, 3) (4, 4) (1, 2) (2, 1) (1, 3) (3,
1) (3, 2) (2, 3)}
No. of elements in
R = 10