JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Sets Relations and Functions

Let

A = {- 2, - 1, 0, 1, 2, 3}

. let R be a relation on A defined by xRy if and only if

y = max {x, 1}

. Let

l

be the number of elements in R . Let m and n be the minimum number of elements required to be added in R to make it reflexive and symmetric relations, respectively. Then

l + m + n

is equal to

(A)12✓ Correct
(B)11
(C)13
(D)14

Answer: (A)

Solution

Each element pairs as

(x, max {x, 1})

, giving

R = {(- 2, 1), (- 1, 1), (0, 1), (1, 1), (2, 2), (3, 3)}

, so

l = 6

. Reflexivity needs

(x, x)

for every element; the missing ones are

(- 2, - 2), (- 1, - 1), (0, 0)

, so

m = 3

. Symmetry needs the reverse of each unequal pair; the missing ones are

(1, - 2), (1, - 1), (1, 0)

, so

n = 3

. Hence

l + m + n = 6 + 3 + 3

, which equals

12

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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