Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_relations

Class 12 Maths · Relations And Functions · Mcq Single Correct #52

For every set \(A\), let \(R\) be any reflexive relation on \(A\), and let \(I=\{(a,a):a\in A\}\). Which statement is always true for every such choice of \(A\) and \(R\)?

(A) \(R\subsetneq I\)
(B) \(I\subseteq R\)
(C) \(R=I\)
(D) None of these

✅ Step-by-Step Solution

Final Answer: Option (B): \(I\subseteq R\)

Reflexivity requires \((a,a)\in R\) for every \(a\in A\), so every pair of \(I\) lies in \(R\): \(I\subseteq R\). Equality is possible but not guaranteed, because a reflexive relation may also contain off-diagonal pairs.

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Class 12 Maths · Relations And Functions · Mcq Single Correct #52

✅ Step-by-Step Solution

Master Chapter 1: Relations And Functions

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