Question

people on a specific diet were examined for vitamin b deficiencies. one person is selected at random.
· let m be the event that the person is deficient in vitamin b₂.
· let n be the event that the person is deficient in vitamin b₆.
which venn diagram is shaded to represent the union of the two events?

Explanation:

Step1: Recall the definition of the union of two events

The union of two events \(M\) and \(N\), denoted as \(M\cup N\), is the set of all outcomes that are in \(M\) or in \(N\) or in both.

Step2: Analyze each Venn - diagram option

• Option A: The shaded region includes all elements of \(M\) (the part of \(M\) that does not overlap with \(N\) and the overlap) and all elements of \(N\) (the part of \(N\) that does not overlap with \(M\) and the overlap). This is consistent with the definition of \(M\cup N\).
• Option B: The non - overlapping part of \(N\) is not shaded. So it does not represent \(M\cup N\).
• Option C: The shaded region is the complement of \(M\cap N\), not \(M\cup N\).
• Option D: The shaded region is only the intersection \(M\cap N\), not \(M\cup N\).

Answer:

A.