Q.

Let R1 be a relation defined by R_1 ={a, b|a≥b, a, b∈R}. Then R1 is

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a

An equivalence relation on R

b

Reflexive, transitive but not symmetric

c

Symmetric, Transitive but not reflexive

d

Neither transitive not reflexive by symmetric

answer is B.

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Detailed Solution

For any a∈R, we have a≥a, therefore the relation R is reflexive but it is not symmetric as (2, 1)∈R but (1, 2)∉R. The relation R is transitive also, because (a, b)∈R, (b, c)∈R imply that a≥b and b≥c which is turn imply that a≥c.
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