Which of the following is an equivalence relation?1)x y3)x−y is divisible by 54)x divides y

xx(false)⇒not symmetricx>y⇒y<x(false)⇒not symmetricx−y divisible by 5⇒ reflexivex−x=0 divisible by 5⇒ Symmetricx−y is divisible by 5 and y−z is divisible by 5so, x−z is also divisible by 5∴equivalent

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Which of the following is an equivalence relation? 1)x<y 2)x>y

Question

Which of the following is an equivalence relation?
1) $x < y$
2) $x > y$
3) $x - y$ is divisible by $5$
4) $x$ divides $y$

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Jack Discussed

Which of the following is an equivalence relation?
1)

x < y

x > y

x - y

is divisible by

5

x

divides

y

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

x < y \Rightarrow y > x (f a l se) \Rightarrow

not symmetric

x > y \Rightarrow y < x (f a l se) \Rightarrow

not symmetric

x - y

divisible by

5 \Rightarrow

reflexive

x - x = 0

divisible by

5 \Rightarrow

Symmetric

x - y

is divisible by

5

and

y - z

is divisible by

5

so,

x - z

is also divisible by

5

∴ e q u i v a l e n t

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Question Text	Which of the following is an equivalence relation? 1) $x < y$ 2) $x > y$ 3) $x - y$ is divisible by $5$ 4) $x$ divides $y$
Answer Type	Text solution:1
Upvotes	150

Which of the following is an equivalence relation?1)x<y2)x>y3)x−y is divisible by 54)x divides y

Text solutionVerified

Practice questions from similar books

Which of the following is an equivalence relation?
1) $x < y$
2) $x > y$
3) $x - y$ is divisible by $5$
4) $x$ divides $y$