For real numbers x and y, we write xRy⇔x−y+√2 is an irrational number. Then the relation R is
A
Reflexive
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B
Symmetric
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C
Transitive
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D
None of these
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Solution
The correct option is A
Reflexive
For any x∈R we have x−x+√2=√2 an irrational number. ⇒xRx for all x. So, R is reflexive.
R is not symmetric, because √2R1 but 1R√2,R is not transitive also because √2R1 and 1R2√2 but √2R2√2.