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Algebra> for real number x and y , defi rne a rela...

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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

Ashlesha Rathi , 11 Years ago

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1 Answers

Jitender Singh

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.

Last Activity: 11 Years ago

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