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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  

Ans.

(2)

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

For symmetric, since (a,b),(b,c)∈R

So, (b,a),(c,b) be in R. For transitive, since (a,b),(b,c)∈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)∈R, so (a,a)∈R should also lie in R.

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

Since (b,c),(c,b)∈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.