Sets & RelationsmediumFree

Sets & Relations: Let Relation Defined

JEE Maths question with a full step-by-step solution.

Question
Let R1R_1 be the relation defined by R1={(a,b)∣a≥b, a,b∈R}R_1 = \{(a, b) \mid a \ge b,\ a, b \in R\}. Then R1R_1 is:
AAn equivalence relation on RR
BReflexive, transitive but not symmetriccorrect
CSymmetric, transitive but not reflexive
DNeither transitive nor reflexive but symmetric
Solution
a≥a⇒R1a \ge a \Rightarrow R_1 is reflexive. a≥ba \ge b and b≥c⇒a≥c⇒R1b \ge c \Rightarrow a \ge c \Rightarrow R_1 is transitive. 2≥12 \ge 1 but 1≱2⇒R11 \not\ge 2 \Rightarrow R_1 is not symmetric. ∴R1\therefore R_1 is reflexive, transitive but not symmetric. Correct answer: (2)
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