Let's solve each part of this question one by one.

Given Information:

• Universal set $\mu = \{3, 4, 5, 6, 7, 8, 9, 10\}$
• Set A $A = \{3, 5, 6, 7, 8\}$
• Set B $B = \{8, 9, 10\}$

Problem Requirements:

1. $A \cap B$ - Intersection of A and B.
2. $A \cap B'$ - Intersection of A with the complement of B.
3. $A' \cap B$ - Intersection of the complement of A with B.

Step 1: Find $B'$ and $A'$

• $B'$: Complement of $B$ in $\mu$ is all elements in $\mu$ but not in $B$.

  • $B' = \{3, 4, 5, 6, 7\}$

• $A'$: Complement of $A$ in $\mu$ is all elements in $\mu$ but not in $A$.

  • $A' = \{4, 9, 10\}$

Now we can proceed with each part.

Solution to Each Part:

Part (i): $A \cap B$

This is the intersection of sets $A$ and $B$.

$A \cap B = \{8\}$

Part (ii): $A \cap B'$

This is the intersection of $A$ with the complement of $B$ (i.e., $B'$).

$A \cap B' = \{3, 5, 6, 7\}$

Part (iii): $A' \cap B$

This is the intersection of the complement of $A$ (i.e., $A'$) with $B$.

$A' \cap B = \{9, 10\}$

Summary of Answers:

1. $A \cap B = \{8\}$
2. $A \cap B' = \{3, 5, 6, 7\}$
3. $A' \cap B = \{9, 10\}$

Would you like further details on any of these steps or have any questions?

Additional Practice Questions:

1. What is $A \cup B$, the union of sets $A$ and $B$?
2. Find $(A \cup B)'$, the complement of the union of $A$ and $B$.
3. Calculate $A \cup B'$, the union of $A$ and the complement of $B$.
4. Determine $A' \cup B'$, the union of the complements of $A$ and $B$.
5. If $C = \{4, 7, 10\}$, find $A \cap C$.

Tip:

When working with set complements, it's helpful to list all elements in the universal set and clearly mark which elements belong to each subset. This makes finding complements and intersections easier.