Question

A is a finite non-empty set. The domain for relation R is the power set of A . (Recall that the power set of A is the set of all subsets of A .) For X⊆A and Y⊆A , X is related to Y if X is a proper subsets of Y (i.e., X⊂Y ). Select the description that accurately describes relation R .

Answer 1

Relation R is best described thus (my own description because your options are absent):

R=[ {¢}, {X:XcY and XcA}, {YcA}, {A} ]

Where {¢} means null or empty set and YcA means Y is a subset of A.

Explanation:

As a finite non-empty set, set A has a definite and countable number of elements.

Relation R is the power set of A hence relation R is the set of all subsets of A.

(Null set is a subset of set A and set A is also a subset of itself; this is why they are included in the power set)

For "X is a subset of or is equal to A" and "Y is a subset of or is equal to A", X is related to Y is X is a subset of Y.

You must have had some options you wanted us to pick from but you didn't post them (probably mistakenly) so I have given the description of relation R as

R=[ {¢}, {X:XcY and XcA}, {YcA}, {A} ] as above. I hope you understand the explanation.

Answer 2

Answer/Step-by-step explanation:

R is defined for all xn: xn(x1, x2, x3, ....) are elements of Y.

X and Y are subsets of A

X contains in Y but Y is not contain in X

There exist elements xn: xn are elements of X and Y

xn are elements of power set of A. That is, xn are elements of X and Y (for X⊆A and Y⊆A)

Where xn are x1, x2, x3, ..... All the elements Y. Since X is a proper subset of Y.