Consider the following Venn diagrams. Each diagram is shaded differently
The Correct Answer and Explanation is :
To solve this task, we need to analyze each of the shaded regions in the provided Venn diagrams and match them with the corresponding set notation. Here’s the explanation of each set notation and the corresponding diagram number:
- (A’ B’) – This set represents the region outside both (A) and (B). That means we are looking for a diagram where neither (A) nor (B) is shaded. Referring to the diagrams:
- Diagram 3 correctly shows the region outside both (A) and (B) shaded, which is (A’ B’).
- (A’B) – This set represents the region where (B) is true but (A) is false. This means the part of (B) that does not overlap with (A) should be shaded.
- Diagram 6 correctly shows only the part of (B) that does not overlap with (A) shaded, which is (A’B).
- (AB’) – This set notation represents the region where (A) is true but (B) is false. Hence, the part of (A) that does not overlap with (B) should be shaded.
- Diagram 4 accurately depicts (AB’), with the area of (A) excluding (B) shaded.
- (AB) – This set is the intersection of (A) and (B), meaning only the overlapping region of (A) and (B) should be shaded.
- Diagram 1 correctly represents (AB), shading only the intersection.
- (A B) – This notation implies the entire regions of both (A) and (B) should be shaded.
- Diagram 5 correctly shows both (A) and (B) entirely shaded, representing (A B).
- (A) – This set represents the entire region of (A) being shaded, irrespective of (B).
- Diagram 2 accurately shades the entire region of (A), fulfilling the set (A).
Now, let’s generate the image to visually represent this explanation, showing a table with the set and the corresponding diagram number for clarity:
Here is the image displaying a table with the set notations and their corresponding Venn diagram numbers, organized as requested. This visual representation can help you see the matching between the set expressions and the Venn diagram numbers clearly.
