NDA 2019 Maths · Mathematics · Sets, Relations and Functions · hard

On the set \1,2,3,4\ the relation R=\(1,2),(2,3),(3,4)\ is given. The least number of ordered pairs that must be added to R to make it transitive is

Single correct option

On the set

\{1,2,3,4\}

the relation

R=\{(1,2),(2,3),(3,4)\}

is given. The least number of ordered pairs that must be added to

R

to make it transitive is

Show answer and solution

Answer: (C) $3$

Transitivity needs

(a,c)

whenever

(a,b),(b,c)\in R

. From

(1,2),(2,3)

we need

(1,3)

; from

(2,3),(3,4)

we need

(2,4)

. Once

(1,3)

is added,

(1,3),(3,4)

forces

(1,4)

. No further pairs arise, so exactly

3

pairs are added. Stopping after the first two direct chains and answering

2

misses the induced pair.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake