Question

For real numbers x and y, define x R y if and only if x – y + root2 is an irrational number. Then the relation R is
(A) reflexive (B) symmetric (C) transitive (D) none of these

Answer 1

For every value of x belongs to R, x−x+

2

i.e.,

2

is an irrational number.

Therefore, it is reflexive.

Now Let's say x=

2

and y=2 then x−y+

2

=2

2

−2 which is irrational but when y=

2

and x=2,

x−y=

2

is not irrational;

∴ it is not symmetric.

Let x−y+

2

is irrational & y−z+

2

is irrational then in above case let x=1; y=

2

×2 & z=

2

Then x−z+

2

is not irrational, therefore the relation is not transitive.

Answer 2

Answer:

Oh Etta..

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