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Let A = { 1,2,3,4,5}. Let R be a relation on A defined ... | Relation (Mathematics) | DivineJEE

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Mathematics

JEE Mains ( $6^{th\ }$ April $2^{nd\ }$ Shift 2024)

Mathematics

Let

A = \{ 1,2,3,4,5\}

. Let

R

be a relation on

A

defined by

xRy

if and only if

4x \leq 5y

. Let

m

be the number of elements in

R

and

n

be the minimum number of dements from

A \times A

that are required to be added to

R

to make it a symmetric relation. Then

m + n

is equal to:

A

24

B

26

C

25

D

23

Correct Answer:

25

Explanation

(c): Given,

A = \left\{ 1,2,3,4,5 \right\}

\\

R = \left\{ (x,y):4x \leq 5y,x,y \in A \right\}

R = \{(1,1),(1,2),(1,3),(1,4),(1,5),(2,2),(2,3),(2,4)

,\\

(2,5),(3,3),(3,4),(3,5),(4,4),(4,5),(5,4),(5,5)\}\therefore\ n(R) = 16 = m

Elements needed to make

R

symmetric

= \{(2,1),(3,1)

,

(4,1),(5,1),(3,2),(4,2),(5,2),(4,3),(5,3)\}

i.e., 9 elements\\

\therefore\ n = 9

So,

m + n = 16 + 9 = 25

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