Set Theory

Here are the solutions to the questions:

1. (a) Set Theory
First, let's list the elements of each set:
$A = \{3, 6, 9\}$ (multiples of 3 less than 12)
$B = \{5, 6, 7\}$ (integers between 4 and 8, exclusive)
$C = \{4, 5, 7\}$

i) Find $A \cap B$
The intersection of A and B contains elements common to both sets.

$$A \cap B = \{6\}$$

ii) Find $(A \cup B) \cap C$
First, find $A \cup B$:
$A \cup B =