Let `R` be the relation on the set R of all real numbers defined by a – InterviewSolution

InterviewSolution

1.	Let `R` be the relation on the set R of all real numbers defined by a `R b` Iff `\|a-b\| le1.` Then `R` isA. reflexive and symmetricB. symmetric onlyC. transitive onlyD. anti-symmetric only
Answer» Correct Answer - A `because\|a-a\|=0lt1impliesaRa,AAainR` `therefore` R is reflexive Again, aRb implies `\|a-b\|le1` `implies \|b-a\|le1impliesbRa` `therefore` R is symmetric. Again, 1 R 2 and 2R1 but `2 ne 1` `therefore` R is not anti-symmetric Further, 1R2 and 2R3 but `1 cancelR 3" "[because\|1-3\|=2gt1]` `therefore` R is not transitive.

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