Q. 174.8( 4 Votes )

Let A = {a, b, c} and the relation R be defined on A as follows R={(a,a), (b, c), (a, b)}. Then, write a minimum number of ordered pairs to be added in R to make it reflexive and transitive.

Answer :

Recall that,


R is symmetric if for all x, y A, if xRy, then yRx.


R is transitive if for all x, y, z A, if xRy and yRz, then xRz.


We have relation R = {(a, a), (b, c), (a, b)} on A.


A = {a, b, c}


For Transitive:


If (a, b) R and (b, c) R


Then, (a, c) R


a, b, c A


For Reflexive:


a, b, c R


Then, (a, a) R


(b, b) R


(c, c) R


We need to add (b, b), (c, c) and (a, c) in R.


We get


R = {(a, a), (b, b), (c, c), (a, b), (b, c), (a, c)}


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