Simplification Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

Simplify the set expression

(A \cup B) \cap (A \cup B')

and justify each step.

1
Apply the distributive law: $(A \cup B) \cap (A \cup B') = A \cup (B \cap B')$ .
2
Since $B \cap B' = \emptyset$ (a set and its complement are disjoint): $A \cup \emptyset = A$ .
3
Therefore $(A \cup B) \cap (A \cup B') = A$ .

Answer

(A \cup B) \cap (A \cup B') = A

Set algebra mirrors Boolean algebra. Distributing union over intersection, then using complementation (

B \cap B' = \emptyset

) and identity (

A \cup \emptyset = A

) simplifies the expression to

A

About Simplification

The process of replacing a complex expression or model with a simpler equivalent that preserves the essential features.

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