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CBSE Class 12-science Answered

Give some examples of relations which is symmetric and transitive but not reflexive.
Asked by Biplab Das | 22 May, 2012, 09:39: PM
answered-by-expert Expert Answer

Let A = {?5, ?6}.

Define a relation R on A as:

R = {(?5, ?6), (?6, ?5), (?5, ?5)}

Relation R is not reflexive as (?6, ?6) ? R.

Relation R is symmetric as (?5, ?6) ? R and (?6, ?5}?R.

It is seen that (?5, ?6), (?6, ?5) ? R. Also, (?5, ?5) ? R.

?The relation R is transitive.

Hence, relation R is symmetric and transitive but not reflexive.
Answered by | 23 May, 2012, 09:33: AM
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