# Let A = {1, 2, 3, 4, 5, 6) and let R = {(a, b) : a, b ∈ A and b = a + 1}.Show that R is (i) not reflexive, (ii) not symmetric and (iii) not transitive.

Given that,

A = {1, 2, 3, 4, 5, 6) and R = {(a, b) : a, b A and b = a + 1}.

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

Now,

R is Reflexive if (a,a) R a A

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

Thus, R is not reflexive .

R is Symmetric if (a,b) R (b,a) R a,b A

We observe that (1,2) R but (2,1) R .

Thus, R is not symmetric .

R is Transitive if (a,b) R and (b,c) R (a,c) R a,b,c A

We observe that (1,2) R and (2,3) R but (1,3) R

Thus, R is not transitive.

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