Let P be the set of factors of 36 and Q be the set of factors of 54. Find P, Q, P 0xC2 0x8A Q, and n(P 0xC2 0x8A Q).

The factors of 36 are the numbers that divide 36 evenly.

$$P = \{1, 2, 3, 4, 6, 9, 12, 18, 36\}$$

The factors of 54 are the numbers that divide 54 evenly.

$$Q = \{1, 2, 3, 6, 9, 18, 27, 54\}$$

The intersection consists of elements that are common to both sets P and Q.

$$P \cap Q = \{1, 2, 3, 6, 9, 18\}$$

Count the number of elements in the set $P \cap Q$.

$$n(P \cap Q) = 6$$

The final answers are:

• (i) $P = \boxed{\{1, 2, 3, 4, 6, 9, 12, 18, 36\}}$ $Q = \boxed{\{1, 2, 3, 6, 9, 18, 27, 54\}}$
• (ii) $P \cap Q = \boxed{\{1, 2, 3, 6, 9, 18\}}$
• (iii) $n(P \cap Q) = \boxed{6}$