Sets Practice Test 1

Concept:De Morgan's law states that the complement of a union is the intersection of the complements.For two sets $X$ and $Y$, this gives $(X' \cup Y')' = X \cap Y$.Explanation:Consider the expression $(X' \cup Y')'$.Apply De Morgan's law to the union inside the complement.$(X' \cup Y')' = (X')' \cap (Y')'$The complement of a complement returns the original set.So, $(X')' = X$ and $(Y')' = Y$.Substitute these back.$(X' \cup Y')' = X \cap Y$This is exactly the intersection of the original sets.Therefore, the correct option is $X \cap Y$.Answer:$X \cap Y$ (Option B).