Let A = {a, b, c} and the relation R be defined on A as follows R = {(

1.	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)}

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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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.

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