JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

Let

R

be the real line. Consider the following subsets of the plane

R \times R:

S=\{(x, y): y=x+1

and

0 < x < 2\},

T=\{(x, y): x-y

is an integer

\}

Which one of the following is true?

View answer and explanation

Correct option: B

T

is an equivalence relation on

R

but

S

is not

The correct answer is B.

T

is an equivalence relation because it is reflexive, symmetric, and transitive, while

S

is not reflexive and thus not an equivalence relation.

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\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

\}

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

S

X

R

X

A

B

R

R

N

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R