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Let R be a relation from set Q to Q def...

Let R be a relation from set Q to Q defined as:
`R={(a,b):a,b in Q and a -b in Z}`
Prove that
(i) For each `a in Q, (a,a) in R`
`(ii) (a,b) in R implies (b,c) in R` where `a, b in Q`
(iii) `(a,b) in R , (b,c) in R implies (a,c) in R ` , where `a, b ,c in Q`

Answer

Step by step text solution for Let R be a relation from set Q to Q defined as: R={(a,b):a,b in Q and a -b in Z} Prove that (i) For each a in Q, (a,a) in R (ii) (a,b) in R implies (b,c) in R where a, b in Q (iii) (a,b) in R , (b,c) in R implies (a,c) in R , where a, b ,c in Q by MATHS experts to help you in doubts & scoring excellent marks in Class 11 exams.

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Knowledge Check

  • Let R be a relation over the set NxxN and it is defined by (a,b)R(c,d)impliesa+d=b+c . Then R is

    A
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    B
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    A
    `R_1` is transitive,`R_2` is not transitive.
    B
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  • Let Z be the set of all integers and let R be a relation on Z defined by a R b implies a ge b. then R is

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    B
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