Let A = \ 0, 3, 4, 6, 7, 8, 9, 10\ and R be the relation defined on A such that R\ (x, y) ∈ A × A: x - yis odd positive integerorx - y = 2\ . The minimum number of elements that must be added to the relation R, so that

Correct answer: 0 Given, Set A = \ 10, 9, 8, 7, 6, 4, 3, 0\ Now relation x - yis odd orx - y = 2 can be given by, \ R = ( 10, 9 ) , ( 10, 8 ) , ( 10, 7 ) , ( 10, 3 ) , ( 9, 8 ) , ( 9, 7 ) , ( 9, 6 ) , ( 9, 4 ) , ( 9, 0 ) , ( 8, 7 ) , ( 8, 6 ) , ( 8, 3 ) , ( 7, 6 ) , ( 7, 4 ) , ( 7, 0 ) , ( 6, 4 ) , ( 6, 3 ) , ( 4, 3 ) , ( 3, 0 )\ So, total there are 19 elements and all the elements of R, ( a, b ) are of type a > b . Hence, we need to add total of 19 more elements to R to make in symmetric

JEE Main 20238 AprilMorning Shift

Exam: JEE Main
Year: 2023
Date: 8 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2023 · 8 April · Morning Shift · Mathematics · Sets and Relations

Let A = \ 0, 3, 4, 6, 7, 8, 9, 10\ and R be the relation defined on...

Let

A = \left\{0, 3, 4, 6, 7, 8, 9, 10\right\}

and

R

be the relation defined on

A

such that

R\left\{\left(x, y\right) \in A \times A: x - y\text{is odd positive integer}\text{or}x - y = 2\right\}

. The minimum number of elements that must be added to the relation

R,

so that it is a symmetric relation, is equal to

_________

Correct answer

Step-by-step solution

Given,
Set A = $\left\{10, 9, 8, 7, 6, 4, 3, 0\right\}$
Now relation $x - y\text{is odd or}x - y = 2$ can be given by,
\left\{R = ( 10, 9 ) , ( 10, 8 ) , ( 10, 7 ) , ( 10, 3 ) , ( 9, 8 ) , ( 9, 7 ) , ( 9, 6 ) , ( 9, 4 ) , ( 9, 0 ) , ( 8, 7 ) , ( 8, 6 ) , ( 8, 3 ) , ( 7, 6 ) , ( 7, 4 ) , ( 7, 0 ) , ( 6, 4 ) , ( 6, 3 ) , ( 4, 3 ) , ( 3, 0 )\right\} $</p><p>So, total there are$ 19 $elements and all the elements of$ R, ( a, b ) $are of type$ a > b $.</p><p>Hence, we need to add total of$ 19 $more elements to$ R to make in symmetric

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