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). Choose the description that accurately describes relation R.
a. Symmetric and Reflexive
b. Anti-symmetric and Reflexive
c. Symmetric and Anti-reflexive
d. Anti-symmetric and Anti-reflexive

Answer 1

Answer:

The answer is "Choice D"

Step-by-step explanation:

Determining the information:

For "$X \subseteq A$ " and "$Y \subseteq A$",  $X$ relates to $Y$ when $X$ and $Y$ has the same cardinality. therefore, R does not have reflective:

For every "$X \subseteq A$", "$X= X$" So, X  not proper subset of$X$.  So, R does not havereflexive.

R does not have symmetry:

For every "$X \subseteq Y$" ,then, "$Y \subset X$"  is not true because $X$ not relate to $Y$.  So, R is not symmetric.

R does not have antisymmetric:

When $X$ relates to $Y$ and $Y$ is relate to $X$, then "$X \subset Y$" and "$Y \subset X$"$\to X=Y$

Therefore, R is anti-symmetric.