Given set $B = \{3, 4, 5\}$, we need to: i. Draw a Venn diagram based on an unspecified set A. Since A is not defined, it cannot be fully represented in a Venn diagram. ii. Find $A \cap B$, the intersection of A and B. iii. Find $A \cup B$, the union of A and B. iv. Find $(A \cap B)^c$, the complement of the intersection of A and B. We assume there is a Universal set given the context.

1. Problem Description

Given set $B = \{3, 4, 5\}$, we need to:

i. Draw a Venn diagram based on an unspecified set A. Since A is not defined, it cannot be fully represented in a Venn diagram.

ii. Find $A \cap B$, the intersection of A and B.

iii. Find $A \cup B$, the union of A and B.

iv. Find $(A \cap B)^c$, the complement of the intersection of A and B. We assume there is a Universal set given the context.

2. Solution Steps

Since Set A is not defined, let's assume a general set A which has an intersection with B, i.e. $A \cap B \neq \emptyset$.

Let's further assume a Universal Set $U$.

i. Venn Diagram:

Draw two overlapping circles. Label one circle as A and the other as B. The set B contains the elements 3, 4, and

5. Therefore write 3, 4, and 5 inside circle B. The overlap between circles A and B represents $A \cap B$. The area of circle A outside the overlap represents the elements in A that are not in B ($A - B$). The area outside both circles but inside $U$ represents $(A \cup B)^c$.

ii. $A \cap B$:

$A \cap B$ is the set of all elements that are in both A and B. Since A is undefined, the intersection cannot be explicitly found, but we can represent it generally as the set of elements common to both. In general, $A \cap B \subseteq B = \{3, 4, 5\}$.

iii. $A \cup B$:

$A \cup B$ is the set of all elements that are in A or B or both. So $A \cup B$ consists of all elements in A together with 3, 4, and

5. It's also not explicitly defined without knowing A.

iv. $(A \cap B)^c$:

$(A \cap B)^c$ is the complement of $A \cap B$, which consists of all elements in the universal set U that are not in $A \cap B$. Formally, $(A \cap B)^c = \{x \in U : x \notin A \cap B\}$. Since A is undefined, it's not possible to explicitly find $(A \cap B)^c$.

3. Final Answer

i. Venn Diagram: A Venn diagram can be drawn showing two overlapping circles labeled A and B, with elements 3, 4, and 5 inside circle B.

ii. $A \cap B$: The intersection $A \cap B$ is a subset of $\{3, 4, 5\}$.

iii. $A \cup B$: $A \cup B$ consists of all elements in A along with the elements 3, 4, and

5.

iv. $(A \cap B)^c$: $(A \cap B)^c$ is the set of all elements in the universal set U that are not in $A \cap B$.