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Archangel Macsika

i) Which type of relation is shown in below expression R1 = { (a,b) | a = b }

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The relation R_1 = \{ (a,b)\ |\ a = b \} is binary. Since (a,a)\in R_1 for any a, this relation is reflexive. If (a,b)\in R_1, then a=b, and hence (b,a)\in R_1, that is the relation is symmetric. If (a,b)\in R_1 and (b,c)\in R_1, then a=b=c, and thus the relation is transitive. Therefore, R_1 is equivalence relation.

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