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 $A = \{x \in R : |x| < 2\}$ and $B = \{x \in R : |x - 2| \geq 3\}$,then:

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

In a class of $55$ students,the number of students studying different subjects are $23$ in Mathematics,$24$ in Physics,$19$ in Chemistry,$12$ in Mathematics and Physics,$9$ in Mathematics and Chemistry,$7$ in Physics and Chemistry and $4$ in all the three subjects. The number of students who have taken exactly one subject is

Which of the following sets is empty?

Which of the following pairs of sets are disjoint?
$(i)$ ${1, 2, 3, 4}$ and ${x : x in mathbb{N}, 4 \leq x \leq 6}$
$(ii)$ ${a, e, i, o, u}$ and ${c, d, e, f}$
$(iii)$ ${x : x \text{ is an even integer}}$ and ${x : x \text{ is an odd integer}}$