construct a venn diagram describing the sets 1. (AuB)n(BuC) 2. (AnB)u(BnC) 3. (CuA)nB 4. B’ u C 5. AnB’ 6. A u B’ u C 7.A n B n C’ 8. A’ n B’ u C 9.An(B’uC) 10. (A’uB) u (BnC) 11. (AuB) n (B’ u C’) 12.(CuA’)nB
The Correct Answer and Explanation is :
Here is the Venn diagram representing the different set operations you requested. Each operation is visually differentiated and labeled accordingly within the diagram.
Explanation of the Venn Diagram:
- (A ∪ B) ∩ (B ∪ C): This represents the elements common to either A or B and either B or C. Visually, it overlaps areas between these sets.
- (A ∩ B) ∪ (B ∩ C): Shows elements that are either in both A and B or in both B and C, covering two overlapping sections.
- (C ∪ A) ∩ B: Includes elements that are either in C or A and also in B, focusing on intersections involving B.
- B’ ∪ C: Includes all elements not in B plus all in C, highlighting areas outside B and including C.
- A ∩ B’: This operation represents elements that are in A but not in B, focusing on parts of A excluding B.
- A ∪ B’ ∪ C: Shows all elements in A, not in B, or in C, covering a broad range of areas.
- A ∩ B ∩ C’: Focuses on elements that are in both A and B but not in C, specifically highlighting their common intersection excluding C.
- A’ ∩ B’ ∪ C: Represents elements not in A and not in B, or in C, indicating a union of exclusions and inclusions involving C.
- A ∩ (B’ ∪ C): Elements in A and either not in B or in C, showing A’s overlap with non-B and C areas.
- (A’ ∪ B) ∪ (B ∩ C): Covers elements not in A or in B, and also elements in both B and C, including a wide area of B and its intersection with C.
- (A ∪ B) ∩ (B’ ∪ C’): Focuses on elements in either A or B and either not in B or not in C, an interesting intersection of unions and exclusions.
- (C ∪ A’) ∩ B: Includes elements either in C or not in A and also in B, highlighting specific overlaps and exclusions.
The diagram provides a visual representation of these operations to aid in understanding their relationships and intersections.