First slide
Relations XII

For real numbers x and y, we write xRyx-y+2 is an irrational number. Then the relation R is


For any xR, we have x-x+2=2 an irrational number.

xRx for all x. So, R is reflexive.

R is not symmetric, because 2R1 but 1R2, R is not transitive also because 2R1 and 1R22 but 2R22.

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