Question

A = {1, 2, 3, 4} minimum number of elements added to make it equivalence relation on set A containing (1, 3) and (1, 2) in it. 

(1) 8 

(2) 9 

(3) 12 

(4) 16

Answer 1

Correct option is (1) 8 

Set A = {1, 2, 3, 4} 

For reflexive relation 

We need to have (1, 1), (2, 2), (3, 3), (4, 4). 

For symmetric, 

(1, 3) ∈ A 

So (3, 1) should be added 

And (1, 2) ∈ A 

So (2, 1) should be added set has become {(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1), (1, 2), (2, 1)} 

Now (3, 1) ∈ A 

(1, 2) ∈ A 

So (3, 2) should be added (for transitive) 

Then (2, 3) should be added (for symmetric) 

So set becomes 

{(1, 1), (2, 2), (3, 3), (4, 4), (1, 3), (3, 1), (1, 2), (2, 1), (3, 2), (2, 3)} 

So minimum 8 elements are added