Cheeck whether the relation R. defined in the set {1,2,3,4,5,6} as R ={(a,b):b=a+1} is reflexive, symmetric or transitive.

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Solution

Let A ={1,2,3,4,5,6}
A relation R is defined on set A is
R ={a,b: b=a+1}. Therefore, R ={(1,2),(2,3),(3,4),(4,5),(5,6)}
Now, $6 ϵ A b u t (6, 6) / ϵ R .$
Therefore, R is not reflexive.
It can be observed that $(1, 2) ϵ R$ but $(2, 1) / ϵ R$ . Therefore, R is not symmetric.
Now, $(1, 2), (2, 3) ϵ R$ but $(1, 3) / ϵ R$ . Therefoe, R is not transitive.
Hence, R is neither reflexive nor symmetric nor transitive.

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