Help me solve the question please? They make me headache.

1. Show

i. $\displaystyle (A' \cup B') \cap (A' \cup B) \cap (A \cup B)=A' \cap B$

ii. $\displaystyle (A \cup B') \cap (A \cup B)=A$

iii. $\displaystyle (A \cup B' \cup C') \cap [A \cup (B \cap C)]=A$

iv. $\displaystyle A \cup (A' \cup B)'=A$

2. A certain sixth form science class consists of 90 pupils, all of whom take mathematics, 45 study chemistry, 42 study biology, and 52 study physics. Of those taking three subjects, 18 study physics and chemistry, 22 study physics and biology, and 16 study chemistry and biology while 5 take all four subjects. Find the number of pupils who study mathematics only.

Answer: 2

Note: I'd like a Venn Diagram and the formula for question 2.