Let I be the set of integers. For a, b ∈ I,a R b if and only if |a – b| < $$1$$, then

Correct option is 3R={(a,a);a∈I}

Questions

Let $I$ be the set of integers. For $a, b \in I$ , $a R b$ if and only if $| a - b | < 1,$ then

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R is not reflexive

R is not symmetric

R={(a,a);a∈I}

R is not an equivalence relation.

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detailed solution

Correct option is C

For any integers a, b, |a – b| < 1 if and onlyif |a – b| = 0 so a = b. Hence R=(a,a);a∈I.Thus R isreflexive, symmetric and transitive.

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Let I be the set of integers. For a, b ∈ I,a R b if and only if |a – b| < 1, then

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

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Let $I$ be the set of integers. For $a, b \in I$ , $a R b$ if and only if $| a - b | < 1,$ then