# 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.

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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