Answer to Question #339711 in Discrete Mathematics for Omar

Question

Determine whether the relation R

on the set of all integers is reflexive,

symmetric, antisymmetric, and/or

transitive, where (x, y)=R if and

only if

X=Y²

Answer 1

Not reflexive because (2, 2) does not satisfy.

Not symmetric because although we can have (9, 3), we can’t have (3, 9).

It is antisymmetric because each integer will map to another integer but not in reverse (except 0 and 1).

Not transitive because if we have (16, 4) and (4, 2), it’s not the case that 16 = 2² .