Give some examples of relations which is symmetric and transitive but not reflexive.

Asked by Biplab Das | 22nd 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  | 23rd May, 2012, 09:33: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.