Question

given the following venn diagram, let blue represent the students taking drama (d) and green represent the students taking math (m). what is n(d u m)?

Explanation:

Step1: Understand the formula for \(n(D\cup M)\)

The formula for the number of elements in the union of two sets \(A\) and \(B\) is \(n(A\cup B)=n(A - B)+n(B - A)+n(A\cap B)\). In the context of the Venn - diagram, for sets \(D\) (drama) and \(M\) (math), \(n(D - M)\) is the number of elements only in \(D\), \(n(M - D)\) is the number of elements only in \(M\), and \(n(D\cap M)\) is the number of elements in both \(D\) and \(M\).

Step2: Identify the values from the Venn - diagram

From the Venn - diagram, \(n(D - M)=2\) (blue non - overlapping part), \(n(D\cap M) = 4\) (the overlapping part), and \(n(M - D)=5\) (green non - overlapping part).

Step3: Calculate \(n(D\cup M)\)

Substitute the values into the formula \(n(D\cup M)=n(D - M)+n(D\cap M)+n(M - D)\).

$$n(D\cup M)=2 + 4+5$$

$$n(D\cup M)=11$$

Answer:

\(11\)