BECE Mathematics 2017 Paper

Concept:A universal set contains all elements under consideration, and the union of all its subsets gives back the universal set itself.Explanation:Option A is false because only the empty set is a subset of the null set; every ordinary set is not a subset of $\emptyset$.Option B is false because the universal set cannot be a subset of the null set.Option C is false because the intersection of two sets is $\emptyset$ only when the sets are disjoint; otherwise it contains their common elements.Option D is true.For example, let $U = \{1, 2, 3\}$.The subsets of $U$ include $\{1\}$, $\{2\}$, $\{3\}$, $\{1,2\}$, $\{2,3\}$, $\{1,3\}$, $\{1,2,3\}$, and $\emptyset$.The union of all these subsets is $\{1, 2, 3\}$, which is exactly $U$.Thus, the universal set is the union of all its subsets.Answer:Option D: The universal set is the union of all its subsets.