The answers are provided but the explanation is confusing. Explain each step more clearly. Show your work.

PARTICIPATION ACTIVITY 3.2.12: Recognizing the properties of a relation: Integer multiples. The domain of relation D is the set of positive integers. For x, y eZ*, xDy if x evenly divides y. Positive integer x evenly divides positive integer y if there is another positive integer n such that y = xn. 1) Is the relation D reflexive, anti-reflexive or neither? Correct O Reflexive O Anti-reflexive For any positive integer x, X = X. 1, so xDx. Therefore D is reflexive. O Neither Correct 2) Is the relation D symmetric, anti-symmetric or neither? O Symmetric O Anti-symmetric O Neither If xDy, then there is a positive integer n such that y = xn. If yDx, then there is a positive integer m such that x = my. Plug my for x into y = xn: y = mny. Since m and n are both positive integers, m= n = 1. Therefore y=x: 1 = x. Thus, xDy and yDx imply that x = y, and Dis anti-symmetric 3) Is the relation D transitive? Correct O Transitive O Not transitive If xDy, then there is a positive integer n such that y = xn. If yDz, then there is a positive integer m such that z = ym. Plug xn for y into z = ym: z = xnm. Since mand n are both positive integers, nm is also a positive integer. Therefore xDz. Thus, xDy and yDz imply that xDz