Let R_1 be a relation defined by R_1 = (a, ,b)|a b, ,a, ,b R . Th… - Vidyadip

MCQ

Let ${R_1}$ be a relation defined by ${R_1} = \{ (a,\,b)|a \ge b,\,a,\,b \in R\} $. Then ${R_1}$ is

A
An equivalence relation on $R$
✓
Reflexive, transitive but not symmetric
C
Symmetric, Transitive but not reflexive
D
Neither transitive not reflexive but symmetric

✓

Answer

Correct option: B.

Reflexive, transitive but not symmetric

b
(b) For any $a \in R$, we have $a \ge a,$ Therefore the relation $R$ is reflexive but it is not symmetric as $(2, 1)$ $ \in R$ but $(1, 2)$ $ \notin R$. The relation $R$ is transitive also, because $(a,b) \in R,(b,c) \in R$ imply that $a \ge b$ and $b \ge c$ which is turn imply that $a \ge c$.

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