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Determine whether Relation R on the set ...

Determine whether Relation `R` on the set `Z` of all integer defined as `R={(x ,\ y): (x-y) =i n t e g e r}` is reflexive, symmetric or transitive.

Text Solution

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`R={(x,y):x−y`is an integer`}`
Now, for every` x∈Z,(x,x)∈R as x−x=0` is an integer.
`\therefore `R is reflexive.
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Knowledge Check

  • R is a relation on the set of N defined as R= {x, y): 2x + y = 24}. Then, the domain of R is:

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    D
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