If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

If $A = \{1, 2, 3, 4, 5\}, B = \{2, 4, 6\}, C = \{3, 4, 6\},$ then $(A \cup B) \cap C$ is

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements and $\bigcup_{r = 1}^{24} X_r = S = \bigcup_{r = 1}^n Y_r$. If each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then $n$ is equal to:

If $U = \{a, b, c, d, e, f\}$,$A = \{a, b, c\}$,$B = \{c, d, e, f\}$,and $C = \{c, d, e\}$,find $(A \cup B) \cup C$.

If $A$ and $B$ are two sets,then $A \cup B = A \cap B$ if and only if:

Let $A = \{1, 3, 5\}$ and $B = \{x : x \text{ is an odd natural number } < 6\}$. Which of the following is false?