1. Problem 26: Draw Venn diagrams for the sets A, B, and C with following expressions: a) $A \cap (B \cup \overline{C})$ b) $\overline{A} \cap \overline{B} \cap \overline{C}$ c) $(A - B) \cup (A - C) \cup (B - C)$ 2. Understanding each part from problem 26: a) $A \cap (B \cup \overline{C})$ means elements in $A$ and also either in $B$ or not in $C$. Think of $B \cup \overline{C}$ as parts that are either in $B$ or outside $C$, then intersect with $A$. b) $\overline{A} \cap \overline{B} \cap \overline{C}$ means elements not in $A$, not in $B$, and not in $C$. This is essentially the region outside all three sets. c) $(A - B) \cup (A - C) \cup (B - C)$ means the union of elements in $A$ but not in $B$, elements in $A$ but not in $C$, and elements in $B$ but not in $C$. This covers all elements in one set but excluded from another. --- 3. Problem 27: Draw Venn diagrams for the sets A, B, and C with following expressions: a) $A \cap (B - C)$: Elements in both $A$ and in $B$ but not in $C$. b) $(A \cap B) \cup (A \cap C)$: Elements in $A$ and $B$ or in $A$ and $C$. c) $(A \cap \overline{B}) \cup (A \cap \overline{C})$: Elements in $A$ and not in $B$, or in $A$ and not in $C$. --- 4. Problem 28: Draw Venn diagrams for sets A, B, C, D with: a) $(A \cap B) \cup (C \cap D)$: Elements in both $A$ and $B$ or both $C$ and $D$. b) $\overline{A} \cup \overline{B} \cup \overline{C} \cup \overline{D}$: Elements not in at least one of the sets $A$, $B$, $C$, or $D$. This is the complement of the union of all four. c) $A - (B \cap C \cap D)$: Elements in $A$ but not in all three $B$, $C$, and $D$ simultaneously. --- All these expressions are set expressions describing parts of the Venn diagrams shaded accordingly. "slug": "set venn diagrams","subject": "set theory","desmos": {"latex": "","features": {"intercepts": false,"extrema": false}},"q_count": 7