Question

the manager of starbucks made a venn diagram to represent customers who ordered beverages.

• let a represent the customers who order cold beverages.
• let b represent the customers who order hot beverages.

which venn diagram represents ( a )?

Explanation:

The complement of set \(A\), denoted as \(A'\), includes all elements that are not in set \(A\). In a Venn - diagram context, this means all regions outside of the circle representing set \(A\).

• Option A: The shaded region includes part of \(A\) and part of the universal set outside \(A\) and \(B\), which is incorrect for \(A'\).
• Option B: The shaded region is the universal set minus the non - overlapping part of \(A\). This represents \(A'\) because \(A'\) is everything not in \(A\).
• Option C: The shaded region is part of \(B\) (non - overlapping with \(A\)), which is not \(A'\).
• Option D: The shaded region is the intersection of \(A\) and \(B\) and part of \(B\), which is not \(A'\).

Answer:

B.