(a) If A = {multiples of 2}, B = {multiples of 3} and C = {factors of 6} are subsets of \(\mu\) = {x: \(1 \leq x \leq 10\)} find A′ \(\cap\) B′ \(\cap\) C′ ...

Answer Details

(a) The universal set is \(\mu = \{1,2,3,4,5,6,7,8,9,10\}\).

• \(A = \{\text{multiples of }2\} = \{2,4,6,8,10\}\)
• \(B = \{\text{multiples of }3\} = \{3,6,9\}\)
• \(C = \{\text{factors of }6\} = \{1,2,3,6\}\)

By De Morgan's law, \(A' \cap B' \cap C' = (A \cup B \cup C)'\).

\[A \cup B \cup C = \{1,2,3,4,6,8,9,10\}.\]

Therefore the elements of \(\mu\) not in this union are:

\[A' \cap B' \cap C' = \{5, 7\}.\]

(b) Buying singly, one ticket costs \(\$18.50\). The bulk price for 5 tickets is \(\$80.00\), shared equally among the 5 people:

\[\text{Cost per person} = \frac{80.00}{5} = \$16.00.\]

Each person's saving compared with buying a single ticket:

\[18.50 - 16.00 = \$2.50.\]

Each person would save \(\mathbf{\$2.50}\).