**Set and Boolean Algebra**Simplify each of the following expressions. Label each identity used. Be mindful that you use the appropriate notation for set algebra or boolean algebra.i. \(((A \cap A^C) \cup (A \cap (A \cup B)))^C\)ii. \(\neg ((\neg P \vee \neg Q) \land Q)\)---**Venn Diagram Shading**Shade the indicated regions of the following Venn diagrams.- Diagram 1: \(((A \cup C) - B) \cup C\)- Diagram 2: \(A^C \cap (B \cup U^C)\)**Explanation of Diagrams:**1. **First Diagram \(((A \cup C) - B) \cup C\):** - Three circles are labeled A, B, and C. - Each circle represents a set. - The task is to shade regions that belong to set \(A \cup C\) excluding set B, and then take the union with set C.2. **Second Diagram \(A^C \cap (B \cup U^C)\):** - Three circles labeled A, B, and C along with the universal set (U). - \(A^C\) represents the complement of set A. - The task is to find the intersection between \(A^C\) and the union of sets B and \(U^C\).

Name: **Set and Boolean Algebra**Simplify each of the following expressions
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: **Set and Boolean Algebra**Simplify each of the following expressions. Label each identity used. Be mindful that you use the appropriate notation for set algebra or boolean algebra.i. \(((A \cap A^C) \cup (A \cap (A \cup B)))^C\)ii. \(\neg ((\neg P