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RELATIONS AND FUNCTIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSRELATIONS AND FUNCTIONS1 Mark
Question
State True or False for the statements.
Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.
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Answer

False.
Solution:
We are given the relation R = {(3, 1), (1, 3), (3, 3)} which is defined on the set A = {1, 2, 3}
Since, $(1,1), (2,2)\notin\text{R}$
Hence, R is not reflexive.
Since, $(3,1), (1,3)\in\text{R}$
Hence, R is symmetric.
Since, $(3,1)\in\text{R}, (1,3)\in\text{R}$ but $(1,1)\notin\text{R}$
Hence, R is not transitive.

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