Question

If A = {1, 2, 3), R= {(1, 2), (1, 1), (2,3)} Then minimum number of elements may be adjoined with the
elements of R so that it may become transitive is
a).
b)1
c)2
d)3​

Answer 1

The minimum number of elements may be adjoined with the elements of R so that it may become transitive is 1

Correct question : If A = {1, 2, 3} , R = {(1, 2), (1, 1), (2,3)} Then minimum number of elements may be adjoined with the elements of R so that it may become transitive is

a) 0 b) 1 c) 2 d) 3

Given :

A = {1, 2, 3} , R = {(1, 2), (1, 1), (2,3)}

To find :

The minimum number of elements may be adjoined with the elements of R so that it may become transitive is

a) 0

b) 1

c) 2

d) 3

Solution :

Step 1 of 2 :

Write down the given set and relation

Here the given set is A = {1, 2, 3}

The relation R is defined on A by

R = {(1, 2), (1, 1), (2,3)}

Step 2 of 2 :

Find the minimum number of elements may be adjoined with the elements of R so that it may become transitive

We know that a relation R on the set A is said to be transitive if for a , b , c ∈ A

(a, b) ∈ R and (b, c) ∈ R implies (a, c) ∈ R

We see that , (1, 2), (2,3) ∈ R but (1,3) ∉ R

In order to make R transitive (1,3) must be an element of R

So the minimum number of elements may be adjoined with the elements of R so that it may become transitive is 1

Hence the correct option is b) 1

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