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The text in the image you provided is:

"4-4 : باستعمال شكل فن (Venn) تحقق مما يلي :
a) (A ∩ B) ̅ = ̅A ∪ ̅B"

This is a mathematical statement that represents one of De Morgan's Laws. It says that the complement of the intersection of two sets \(A\) and \(B\) is equal to the union of their complements:

\[
\overline{A \cap B} = \overline{A} \cup \overline{B}
\]

To verify this, you can use a Venn diagram to visually represent the sets \(A\), \(B\), and their intersections/unions. Here's the step-by-step explanation:

1. **\(A \cap B\)** represents the elements common to both sets \(A\) and \(B\) (the intersection).
2. **\(\overline{A \cap B}\)** represents the complement of the intersection, which includes all elements *not* in the intersection of \(A\) and \(B\).
3. According to De Morgan’s Law, this complement is equivalent to the union of the complements of \(A\) and \(B\), i.e., **\(\overline{A} \cup \overline{B}\)**, which means all elements that are either *not* in \(A\) or *not* in \(B\).

This can be visualized by shading the appropriate regions in a Venn diagram to show that both sides of the equation are equivalent.

Would you like further details or visual clarification on how to create the Venn diagram for this?

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Here are 5 related questions to help deepen understanding:

1. What are the other De Morgan's laws in set theory?
2. How do we represent set operations like union, intersection, and complement in Venn diagrams?
3. Can you explain how set theory applies to logic and truth tables?
4. How would De Morgan's laws be used in Boolean algebra?
5. What is the relationship between set complement and the universal set?

**Tip:** Always start by understanding the fundamental set operations (union, intersection, and complement) before diving into more complex laws like De Morgan's. This will make the concepts easier to visualize and apply.

باستعمال شكل فن (Venn) تحقق مما يلي : (A ∩ B) ̅ = ̅A ∪ ̅B

Learn how to use Venn diagrams to verify De Morgan's Law, specifically how the complement of A ∩ B equals the union of the complements of A and B. This detailed breakdown covers set theory and key principles of De Morgan's Laws. Suitable for high school students (Grades 10-12).

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