Check if the relation R on the set A = { 1, 2, 3, 4, 5, 6 } defined as R = { (x, y) : y is divisible by x } is (i) symmetric (ii) transitive

 

 
 
 
 
 

Answers (1)
S safeer

A = {1, 2, 3, 4, 5, 6}

R = {(x, y) : y is divisible by x} 

i)

\\ $ Check for Symmetric: $ \\ $ if $ (\mathrm{a}, \mathrm{b}) \in \mathrm{R}$ $ then $ (\mathrm{b}, \mathrm{a}) \in \mathrm{R} $\Rightarrow \mathrm{R}$ is Symmetric $

\\$Here $ \operatorname{As}(1,2) \in R$ but (2,1)$\notin R \Rightarrow R$ is not symmetric

ii)

\\ $ Check For transitive : $ \\ $ If $(a, b),(b, c) \in R $ then $ (a, c) \in R \Rightarrow $ R is transitive $

b=ka , c = lb

c = kla

\Rightarrow $ c is divisible by a

$ R is transitive.

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