Let W denotes the words in the English dictionary. If the relation R is given by R = (x, y) ∈ W × W: thewordxandyhaveatleastoneletterincommon , then R is

Correct answer: A. reflexive, symmetric and not transitive Given, R = ( x, y ) ∈ W × W: the word x and y have atleast one letter in common Let, W = cat, toy, you, Clearly, R is reflexive and symmetric but not transitive. [Since, catRtoy, toyRyou ⇏ catRyou ]

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Sets and Relations

NTA Abhyas 2020 · Mathematics · Sets and Relations

Let W denotes the words in the English dictionary. If the relation...

Let

W

denotes the words in the English dictionary. If the relation

R

is given by

R = { \left(x, y\right) \in W \times W: thewordxandyhaveatleastoneletterincommon } ,

then

R

Options

Areflexive, symmetric and not transitive
Breflexive, symmetric and transitive
Creflexive, not symmetric and transitive
Dnot reflexive, symmetric and transitive

Correct answer

A. reflexive, symmetric and not transitive

Step-by-step solution

Given,

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

the word

x

and

y

have atleast one letter in common}

Let,

W = { cat, toy, you, \ldots }

Clearly,

R

is reflexive and symmetric but not transitive.

[Since,

catRtoy, toyRyou ⇏ catRyou

]

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