The probability that a relation $R$ from $\{x, y\}$ to $\{x, y\}$ is both symmetric and transitive, is equal to

JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

The probability that a relation

R

from

\{x, y\}

\{x, y\}

is both symmetric and transitive, is equal to

View answer and explanation

Correct option: A

\frac{5}{16}

Option A (

\frac{5}{16}

) is correct because there are 5 relations that are both symmetric and transitive out of a total of 16 possible relations.

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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

\}

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