Question 15: What does the notation (A extrm U B)' represent? Question 16: If 45% use bus, 30% bicycle, 25% walk, 10% bus & bicycle, 8% bicycle & walk, 12% bus & walk, and 2% all three, what percentag

15. C. Outside both A and B

The notation $(A \cup B)'$ represents the complement of the union of sets $A$ and $B$.

• The union $A \cup B$ includes all elements that are in set $A$, or in set $B$, or in both.
• The complement $(A \cup B)'$ therefore includes all elements that are not in $A \cup B$. This means elements that are neither in $A$ nor in $B$, which corresponds to the region outside both $A$ and $B$ in a Venn diagram.

16. A. 25%

Let $B$ represent students who use the bus, $C$ for bicycle, and $W$ for walk. We are given the following percentages:

• $n(B) = 45\%$
• $n(C) = 30\%$
• $n(W) = 25\%$
• $n(B \cap C) = 10\%$ (bus and bicycle)
• $n(C \cap W) = 8\%$ (bicycle and walk)
• $n(B \cap W) = 12\%$ (bus and walk)
• $n(B \cap C \cap W) = 2\%$ (all three modes)

To find the percentage of students who use only the bus, we use the formula:

$$n(B \text{ only}) = n(B) - n(B \cap C) - n(B \cap W) + n(B \cap C \cap W)$$