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Question

Relation R in the set A of human beings in a town at a particular time given by R={(x,y):xandyliveinthesamelocality}

enter 1-reflexive and transitive but not symmetric
2-reflexive only
3-Transitive only
4-Equivalence
5-None

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Solution

R={(x,y):x and y live in the same locality}

Clearly (x,y)R as x and x is the same human being.

R is reflexive.

If (x,y)R, then x and y live in the same locality.

y and x live in the same locality.

(y,x)R

R is symmetric.

Now, let (x,y)R and (y,z)R.

x and y live in the same locality and y and z live in the same locality.

x and z live in the same locality.

(x,z)R

R is transitive.

Hence, R is reflexive, symmetric and transitive.

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