15. If A = {2, 3, 4, 5} B = {4, 5, 6, 7} C = {6, 7, 8, 9} D = {8, 9, 10, 11},Find:a) A Ս B (1 mark)b) C ∩ D

1. Break Down the Problem

We have four sets:

• $A = \{2, 3, 4, 5\}$
• $B = \{4, 5, 6, 7\}$
• $C = \{6, 7, 8, 9\}$
• $D = \{8, 9, 10, 11\}$

We need to find: a) The intersection of sets $A$ and $B$: $A \cap B$

b) The intersection of sets $C$ and $D$: $C \cap D$

2. Relevant Concepts

The intersection of two sets $X$ and $Y$, denoted as $X \cap Y$, is defined as the set of elements that are common to both $X$ and $Y$.

3. Analysis and Detail

a) Finding $A \cap B$:

• Elements of set $A$: $\{2, 3, 4, 5\}$
• Elements of set $B$: $\{4, 5, 6, 7\}$

Common elements:

• $4$ is in both $A$ and $B$.
• $5$ is in both $A$ and $B$.

Thus, $A \cap B = \{4, 5\}$

b) Finding $C \cap D$:

• Elements of set $C$: $\{6, 7, 8, 9\}$
• Elements of set $D$: $\{8, 9, 10, 11\}$

Common elements:

• $8$ is in both $C$ and $D$.
• $9$ is in both $C$ and $D$.

Thus, $C \cap D = \{8, 9\}$

4. Verify and Summarize

We have verified the common elements in both intersections by examining the contents of each set. The calculations confirm that the common elements for each intersection are accurate.

Final Answer

a) $A \cap B = \{4, 5\}$

b) $C \cap D = \{8, 9\}$