Exercise 8b Given that X = Whole numbers less than 24, P = Prime numbers less than 24, Q = Even numbers less than 24. Find (a) P ∩ Q, (b) P ∪ Q, (c) P' ∩ Q, (d) (P ∪ Q)'

• $Q = \{\text{all perfect squares less than } 30\}$ The perfect squares are $1^2=1$, $2^2=4$, $3^2=9$, $4^2=16$, $5^2=25$. The next is $6^2=36$, which is not less than 30. So, $Q = \{1, 4, 9, 16, 25\}$.
• $P = \{\text{all odd numbers from } 1 \text{ to } 10\}$ The odd numbers between 1 and 10 (inclusive) are 1, 3, 5, 7, 9. So, $P = \{1, 3, 5, 7, 9\}$.

This is the set of elements common to both Q and P.

The answer for (i) is $\boxed{\{1, 9\}}$.

This is the set of all elements in Q or P (or both).

The answer for (ii) is $\boxed{\{1, 3, 4, 5, 7, 9, 16, 25\}}$.

First, we use the result for $P \cup Q$ from Step 3:
$P \cup Q = \{1, 3, 4, 5, 7, 9, 16, 25\}$.
Now, we find the intersection of this set with the empty set $\phi$. The intersection of any set with the empty set is always the empty set.

The answer for (iii) is $\boxed{\phi}$.