First slide

Relations XII

Question

$The relation R = {(a, b) / a, b \in Z and ax = b for some x \in Z} is$

Easy

A

Equivalence
B

Reflexive but not transitive
C

Symmetric
D

Reflexive, symmetric but not transitive

Solution

$a \cdot 1 = a \Rightarrow (a, a) \in R$
Hence, R is reflexive
$(a, 0) \in R, but (0, a) \notin R$
Hence, R is not symmetric
$(a, b), (b, c) \in R \Rightarrow (a, c) \in R$
Hence R is transitive

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