Let $ \mathrm{N} $ denote the set of all natural numbers. Define two binary relations on $ N $ as $ R_{1}=\{(x, y) \in N \times N: 2 x+y=10\} $ and $ R_{2}=\{(x, y) \in N \times N: x+2 y=10\} $. Then

Range of $ R_{2} $ is $ \{1,2,3,4\} $

Both $ R_{1} $ and $ R_{2} $ are transitive relations

Both $ R_{1} $ and $ R_{2} $ are symmetric relations

Range of $ R_{1} $ is $ \{2,4,8\} $

JEE MATHEMATICS MCQ: RELATIONS

1 Medium

1 of 1

Understanding +4 | -1

Let

\mathrm{N}

denote the set of all natural numbers. Define two binary relations on

N

R_{1}=\{(x, y) \in N \times N: 2 x+y=10\}

and

R_{2}=\{(x, y) \in N \times N: x+2 y=10\}

. Then

View answer and explanation

Correct option: C

Range of

R_{2}

\{1,2,3,4\}

Option C is correct because the range of R2, defined by x + 2y = 10, with x and y being natural numbers, is {1, 2, 3, 4}.

Practice All Chapter MCQs →

\mathrm{Z}

R

\mathrm{N}

\mathrm{R}

\mathrm{N} \times \mathrm{N}

(\mathrm{a}, \mathrm{b}) \mathrm{R}(\mathrm{c}, \mathrm{d})

a d(b+c)=b c(a+d)

\mathrm{R}

W

R

R=\{(x, y) \in W \times W \mid

x

y

\}

S

R = \{ \left( {a,\;b} \right):1 + ab > 0\}

S

X

R

X

A

B

R

R

N

R = \left\{ {\left( {x,\;y} \right):4x + 3y = 20} \right\}

R