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
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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