Question

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

Given, the relation R defined on the set A={1,2,3,4,5,6} as R={(a,b):b=a+1}.

The relation is not reflexive as a

=a+1, for any a∈A.

Also 3=2+1 but 2

=3+1 i.e. (2,3)∈R but (3,2)

∈R, so the relation is not symmetric.

Now, (2,3)∈R,(3,4)∈R but (2,4)

∈R since 3=2+1,4=3+1 but 4

=2+1.

So the relation is not transitive also.

Answer 2

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