List elements of sets A and B, find their intersection and union, and illustrate on a Venn diagram.

$U = \{\text{Odd numbers less than 19}\}$
$U = \{1, 3, 5, 7, 9, 11, 13, 15, 17\}$

$A = \{\text{Factors of 15}\}$
The factors of 15 are the numbers that divide 15 exactly.
$A = \{1, 3, 5, 15\}$

$B = \{\text{Prime numbers}\}$ (within $U$)
Prime numbers in $U$ are numbers greater than 1 that are only divisible by 1 and themselves.
$B = \{3, 5, 7, 11, 13, 17\}$
The elements in set A are $\boxed{\{1, 3, 5, 15\}}$ and in set B are $\boxed{\{3, 5, 7, 11, 13, 17\}}$.

$A \cap B$ contains elements common to both $A$ and $B$.
$A = \{1, 3, 5, 15\}$
$B = \{3, 5, 7, 11, 13, 17\}$
$A \cap B = \{3, 5\}$

$A \cup B$ contains all elements in $A$ or $B$ (or both).
$A \cup B = \{1, 3, 5, 7, 11, 13, 15, 17\}$
The set $A \cap B$ is $\boxed{\{3, 5\}}$ and $A \cup B$ is $\boxed{\{1, 3, 5, 7, 11, 13, 15, 17\}}$.

• $A \cap B = \{3, 5\}$ (in the overlap)
• Elements in $A$ only: $A \setminus B = \{1, 15\}$
• Elements in $B$ only: $B \setminus A = \{7, 11, 13, 17\}$
• Elements in $U$ but not in $A$ or $B$: $U \setminus (A \cup B) = \{9\}$

      U
+---------------------------------+
|         +-------+   +-------+   |
|         | A     |   | B     |   |
|         | {1,15}|   | {7,11,|   |
|         |    +--+---+--+    |   |
|         |    |3,5|   |    |   |
|         |    +--+---+--+    |   |
|         |       |   |13,17}|   |
|         +-------+   +-------+   |
|                                 |
|             {9}                 |
+---------------------------------+

The prime factors of 15 are 3 and 5.

The elements 3 and 5 are in the intersection of sets $A$ and $B$ ($A \cap B$).

1. b) Find the value of $x$ if $3^{x-1} = 27$.

The value of $x$ is $\boxed{4}$.

2. a) Determine the combination of GH¢20, GH¢50, GH¢100, GH¢200 and GH¢500 notes to make GH¢1,000,000.
This question asks for a combination. Here is one possible combination:

Number of GH¢500 notes = $\frac{\text{GH}\text{¢}500,000}{\text{GH}\text{¢}500} = 1,000$ notes.
Remaining amount = $\text{GH}\text{¢}1,000,000 - \text{GH}\text{¢}500,000 = \text{GH}\text{¢}500,000$.

Number of GH¢2