Answer :

Let us take A = {1, 2, 3, 4, 5, 6}

A relation R is defined on set A as:


R = {(a, b): b = a + 1}


Then, R = {(1,2), (2,3), (3,4), (4,5), (5,6)}


Now, we will find (a, a) R, where a ϵ A


For instance,


(1,1), (2,2), (3,3), (4,4), (5,5), (6,6) R


Therefore, R is not reflexive.


We can see that (1,2) ϵ R, but (2,1) R.


Therefore, R is not symmetric.


And now, (1,2), (2,3) ϵ R


But, (1,3) R


Therefore, R is not transitive.


Therefore, R is neither reflexive, nor symmetric, nor transitive.


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