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For real numbers x and y, we write x* y,...

For real numbers x and y, we write` x* y`, if `x - y +sqrt2` is an irrational number. Then, the relation ` *` is an equivalence relation.

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For each value of `x ∈ R`, `x − x + √2` that is `√2` is an irrational number.
It is reflexive.
Let `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
...
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  3. If R is the largest equivalence relation on a set A and S is any relat...

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  12. In the set Z of all integers, which of the following relation R is not...

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  13. Let A={1,\ 2,\ 3} and consider the relation R={(1,\ 1),\ (2,\ 2),\ (3,...

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  14. The relation S defined on the set R of all real number by the rule a\ ...

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  15. The maximum number of equivalence relations on the set A = {1, 2, 3} a...

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  16. Let R be a relation on the set N of natural numbers defined by n\ R\ m...

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  20. For real numbers x and y, we write x* y, if x - y +sqrt2 is an irratio...

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