JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Sets Relations and Functions

Let

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

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

2 x - y \in {0, 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)18
(B)17✓ Correct
(C)15
(D)16

Answer: (B)

Solution

The ordered pairs with

2 x - y \in {0, 1}

and both coordinates in

A

are

(- 1, - 2), (- 1, - 3), (0, 0), (0, - 1), (1, 2), (1, 1), (2, 3)

, so

ℓ = 7

. Reflexivity needs

(x, x)

for every element of

A

; only

(0, 0)

and

(1, 1)

are present, so five pairs must be added and

m = 5

. Symmetry needs the reverse of each unequal pair, namely

(- 2, - 1), (- 3, - 1), (- 1, 0), (2, 1), (3, 2)

, giving

n = 5

. Hence

ℓ + m + n = 7 + 5 + 5 = 17

JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 04 Apr 2025 · Shift 2 · Sets Relations and Functions

Solution

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