The relation ★ is defined on Z-{0} by xy if and only if every prime divisor of x is a divisor of y. For each of the questions below, be sure to provide a proof supporting your answer. a) Is reflexive? b) Is c) Is d) Is transitive? ) Is ★ an equivalence relation, a partial order, both, or neither? symmetric? anti-symmetric?

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The relation ★ is defined on Z-{0} by
x ★y if and only if every prime divisor of x is a divisor of y.
For each of the questions below, be sure to provide a proof supporting your answer.
a) Is reflexive?
b) Is ★ symmetric?
c) Is ★ anti-symmetric?
d) Is transitive?
¹) Is ★ an equivalence relation, a partial order, both, or neither?
Transcribed Image Text:The relation ★ is defined on Z-{0} by x ★y if and only if every prime divisor of x is a divisor of y. For each of the questions below, be sure to provide a proof supporting your answer. a) Is reflexive? b) Is ★ symmetric? c) Is ★ anti-symmetric? d) Is transitive? ¹) Is ★ an equivalence relation, a partial order, both, or neither?
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