Which of the following describes X U (Y ∩ Z)?

Question

ScanSolve AI Tutor · Accepted Answer

To determine which Venn diagram describes $X \cup (Y \cap Z)$ , we need to break down the expression:

Identify the innermost operation.
The innermost operation is $Y \cap Z$ . This represents the region where sets Y and Z overlap.
Identify the outer operation.
The outer operation is $X \cup (Y \cap Z)$ . This means we need to shade the entire set X, and also include the region identified in Step 1 ( $Y \cap Z$ ).
Combine the regions.
So, the shaded area should include all of circle X, plus the specific region where Y and Z intersect.
Compare with the given options.
- Option A shades only the intersection of all three sets ( $X \cap Y \cap Z$ ).
- Option B shades the intersection of X and Y, and the intersection of Y and Z.
- Option C has no shading.
- Option D shades the intersection of X and Z, and the intersection of Y and Z.
- Option E shades the entire circle X and the region where Y and Z overlap. This matches our description from Step 3.
The final answer is $\text{E}$

Answer