Let $W$ denote the words in the English dictionary. Define the relation $R$ by $R=\{(x, y) \in W \times W$ : the words $x$ and $y$ have at least one letter is common$\}.$ Then, $R$ is

Not reflexive, symmetric and transitive

Reflexive, not symmetric and transitive

Reflexive, symmetric and transitive.

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JEE MATHEMATICS MCQ: RELATIONS

1 Easy

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Analyzing +4 | -1

Let

W

denote the words in the English dictionary. Define the relation

R

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

: the words

x

and

y

have at least one letter is common

\}.

Then,

R

View answer and explanation

Correct option: B

Reflexive, symmetric and not transitive

The correct answer is B. The relation

R

is reflexive and symmetric but not transitive because having a common letter between two pairs of words doesn't guarantee a common letter between the first and last word.

More Questions from RELATIONS

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In the set

\mathrm{Z}

of all integers, which of the following relation

R

is not an equivalence relation? Let

\mathrm{N}

denote the set of all natural numbers and

\mathrm{R}

be the relation on

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

defined by

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

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

, then

\mathrm{R}

is Let

W

denote the words in the English dictionary. Define the relation

R

by:

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

the words

x

and

y

have at least one letter in common

\}

Let

S

be the set of all real numbers. Then, the relation

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

S

is Let

X

be a family of sets and

R

be a relation on

X

defined by '

A

is disjoint from

B

'. Then

R

is:

R

is relation on

N

given by

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

. Which of the following belongs to

R