Question

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

Answer 1

Answer:

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

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=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)

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∈R since 3=2+1,4=3+1 but 4

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=2+1.

So the relation is not transitive also.