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Which of the following is not an equivalence relation on Z?

Question

Which of the following is not an equivalence relation on $Z$ ?

a R b \Leftrightarrow a + b

is an even integer

a R b \Leftrightarrow a - b

is an even integer

a R b \Leftrightarrow a < b

a R b \Leftrightarrow a = b

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Which of the following is not an equivalence relation on

Z

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Text solutionVerified

Among the Options

Opt : [C]

a R b \Leftrightarrow a < b

As,

a < b

doesn't imply

b < a

,which make the relation asymmetric and thus it is not an equivalence relation .

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Question Text	Which of the following is not an equivalence relation on $Z$ ?
Answer Type	Text solution:1
Upvotes	150