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 :

• A. 3
• B. 7
• C. 4
• D. 5

Answer 1

Answer: (B)

7

Answer 2

For Symmetric (a,b),(b,c)∈R ⇒(b,a),(c,b)∈R
For Transitive (a,b),(b,c)∈R ⇒(a,c)∈R
Now
1. Symmetric
∴(a,c)∈R⇒(c,a)∈R
2. Transitive
∴(a,b),(b,a)∈R
⇒(a,a)∈R&(b,c),(c,b)∈R
⇒(b,b)&(c,c)∈R
∴ Elements to be added
{(b,a),(c,b),(a,c),(c,a),(a,a),(b,b),(c,c)}
Number of elements to be added =7