The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric and transitive is [2023]

Question

The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric and transitive is [2023]

Smart Achievers · Accepted Answer

(2)

Given relation, $R = {(a, b), (b, c)}$ and set = ${a, b, c}$

For symmetric, since $(a, b), (b, c) \in R$

So, $(b, a), (c, b)$ be in R. For transitive, since $(a, b), (b, c) \in R$

So, $(a, c)$ should be in R. Then $(c, a)$ should also be in R since $(a, c)$ lies in R.

Since $(a, b), (b, a) \in R$ , so $(a, a) \in R$ should also lie in R.

Since $(c, b), (b, c) \in R$ , so $(c, c)$ should also lie in R.

Since $(b, c), (c, b) \in R$ , so $(b, b)$ should also lie in R.

$∴$ Elements to be added are:

$(b, a), (c, b), (a, c), (c, a), (a, a), (c, c), (b, b)$ .

Total number of elements to be added = 7.

Solution

Q.
The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric and transitive is [2023]

1 3

2 7

3 4

4 5

Want Us to Email you About Special Offers & Updates?

Solution

Q. The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric and transitive is [2023]

1 3

2 7

3 4

4 5

Want Us to Email you About Special Offers & Updates?

Q.
The minimum number of elements that must be added to the relation R = {(a, b), (b, c)} on the set {a, b, c} so that it becomes symmetric and transitive is [2023]