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

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Solution

We have,

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

R can be a reflexive relation only when elements (b, b) and (c, c) are added to it

R can be a transitive relation only when the element (a, c) is added to it

So, the minmum number of ordered pairs to be added in R is 3.

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

We have, A = {a, b, c} and R = {(a, a), (b, c), (a, b)} R can be a reflexive relation only when elements (b, b) and (c, c) are added to it R can be a transitive relation only when the element (a, c) is added to it So, the minmum number of ordered pairs to be added in R is 3.

We have,

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

R can be a reflexive relation only when elements (b, b) and (c, c) are added to it

R can be a transitive relation only when the element (a, c) is added to it

So, the minmum number of ordered pairs to be added in R is 3.