Sets & Relations
Image set of a relation
nta_pyq_2025_apr
Grade 12
Question:
Let$A = {-2$, -1, 0, 1, 2, 3}. let R be a relation$o_n$A defined by xRy if and only if$y = max{x$, 1}. Let l be the number of elements\in \mathbb{R}. Let m and n be the minimum number of elements required to be added\in \mathbb{R} to make it reflexive and symmetric relations, respectively. Then$l + m + n$is equal to
Step-by-Step Solution
Key Concept: Translate the finite relation rule into explicit admissible ordered pairs and count the required set.
$A = {-2$, -1, 0, 1, 2, 3} (1)$R = {(-2$, 1),$(-1$, 1), (0, 1), (1, 1), (2, 2), (3, 3)} ℓ = 6$m = 3$$n = 3$ℓ +$m + n = 12$
Correct Answer: 1