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The problem asks to represent the following set operations using Venn diagrams:

1. \((A \cap B)' \cap C\)
2. \((A \cap B) \cup (A' \cap B')\)

Let's break down each set expression before illustrating how to represent them in a Venn diagram:

### 1. \((A \cap B)' \cap C\)
- \(A \cap B\) is the intersection of sets \(A\) and \(B\), which means the elements common to both \(A\) and \(B\).
- \((A \cap B)'\) is the complement of \(A \cap B\), meaning everything outside the intersection of \(A\) and \(B\).
- The final expression \((A \cap B)' \cap C\) represents the elements that are in \(C\) but not in the intersection of \(A\) and \(B\).

### 2. \((A \cap B) \cup (A' \cap B')\)
- \(A \cap B\) is the intersection of \(A\) and \(B\).
- \(A' \cap B'\) represents the intersection of the complements of \(A\) and \(B\), i.e., the elements that are outside both \(A\) and \(B\).
- The union \((A \cap B) \cup (A' \cap B')\) includes all elements either in the intersection of \(A\) and \(B\) or outside both \(A\) and \(B\).

Would you like me to generate the Venn diagrams for these expressions?

Show the following sets using Venn diagrams: 1. (A ∩ B)' ∩ C 2. (A ∩ B) ∪ (A' ∩ B')

This page explains how to represent the set operations (A ∩ B)' ∩ C and (A ∩ B) ∪ (A' ∩ B') using Venn diagrams. Explore concepts like intersection, union, and complements in set theory. Suitable for students in Grades 9-11.

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