Let $U$ be the universal set and $A \cup B \cup C = U$. Then $\{ (A - B) \cup (B - C) \cup (C - A)\} '$ is equal to

Let $U = \{1, 2, 3, 4, 5, 6\}$,$A = \{2, 3\}$,and $B = \{3, 4, 5\}$. Find $A'$,$B'$,$A' \cap B'$,$A \cup B$,and hence show that $(A \cup B)' = A' \cap B'$.

For each positive real number $\lambda$,let $A_\lambda$ be the set of all natural numbers $n$ such that $|\sin(\sqrt{n+1}) - \sin(\sqrt{n})| < \lambda$. Let $A_\lambda^c$ be the complement of $A_\lambda$ in the set of all natural numbers. Then,

Let $A$ and $B$ be two non-empty subsets of a set $X$ such that $A$ is not a subset of $B$,then

If $U = \{a, b, c, d, e, f, g, h\}$,find the complement of the set $A = \{a, b, c\}$.

If $U = \{a, b, c, d, e, f, g, h\}$,find the complement of the set $B = \{d, e, f, g\}$.