Consider the relation R on the set of all real numbers defined by R = {(a, b) : |a − b| ≤ 0}. R is: A. reflexive and symmetric but not transitive B. reflexive and transitive but not symmetric C. only reflexive D. an equivalence relation Answer: D) an equivalence relation Explanation: |a − b| ≤ 0 implies a = b. So R = {(a, a) : a ∈ R}, the identity relation, which is an equivalence relation.

imo class 12 relations and functions

Consider the relation R on the set of all real numbers defined by R = {(a, b) : |a − b| ≤ 0}. R is:

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Consider the relation R on the set of all real numbers defined by R = {(a, b) : |a − b| ≤ 0}. R is:

Answer: D) an equivalence relation

Explanation: |a − b| ≤ 0 implies a = b. So R = {(a, a) : a ∈ R}, the identity relation, which is an equivalence relation.