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for real number x and y , defi rne a relationR, xR y if and only if x-y+2 1/2 is an iirational number.then the relation R is

for real number x and y , defi rne a relationR, xR y if and only if x-y+21/2  is an iirational number.then the relation R is

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1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find solution to your question below
x, y \in R
Relation is defined
x R y such that
x – y + (2)1/2is an irrational number.
Let a to be an irrational number.
Then,
x - y + \sqrt{2} = a
y = x + \sqrt{2}-a
This is similar to straight line.
So for every input, there is one output
So, R is one – one relation.
Since range is equal to co domain, R is onto also.
Finaaly, R is one – one & onto relation.


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