1. **Problem Statement:** Given the universal set $U = \{a, b, c, d, e, f, g, h\}$ and set $B = \{a, b, c, f\}$, we are asked to: (a) Draw a Venn diagram showing the relationship between $B$ and $U$. (b) List the complement of set $B$. (c) State the relationship between set $U$ and set $B$ based on the Venn diagram. 2. **Step (a): Drawing the Venn Diagram** - The universal set $U$ is represented as a rectangle containing all elements $\{a, b, c, d, e, f, g, h\}$. - Set $B$ is a subset of $U$, represented as a circle inside the rectangle containing elements $\{a, b, c, f\}$. - Elements in $U$ but not in $B$ lie outside the circle but inside the rectangle. 3. **Step (b): Complement of Set $B$** - The complement of $B$, denoted $B^c$, is the set of elements in $U$ that are not in $B$. - Using set difference: $$B^c = U \setminus B = \{d, e, g, h\}$$ 4. **Step (c): Relationship Between $U$ and $B$** - Since $B$ is a subset of $U$, every element of $B$ is contained in $U$. - The Venn diagram shows $B$ as a circle fully inside the rectangle $U$. - Therefore, $B \subseteq U$. **Final answers:** - (a) Venn diagram with $B$ inside $U$. - (b) $B^c = \{d, e, g, h\}$. - (c) $B$ is a subset of $U$, i.e., $B \subseteq U$.