Question

westside high’s 2015 senior - class science enrollment is summarized by the venn diagram. chemistry, biology, and physics class enrollments are denoted by the sets c, b, an p, respectively. how many students are in the 2015 senior class? how many students are taking chemistry and biology, but not physics? how many students are not taking science?

Explanation:

First Question: How many students are in the 2015 senior class?

Step1: Identify all regions

The universal set \( U \) includes the regions: only \( C \) (9), only \( B \) (11), only \( P \) (7), \( C \cap B \) only (5), \( C \cap P \) only (6), \( B \cap P \) only (4), \( C \cap B \cap P \) (3), and the region outside all three (18).

Step2: Sum all regions

Sum all these values: \( 9 + 11 + 7 + 5 + 6 + 4 + 3 + 18 \)
First, add the single - set regions: \( 9+11 + 7=27 \)
Then, add the two - set only regions: \( 5 + 6+4 = 15 \)
Then add the three - set region: \( 3 \)
Then add the outside region: \( 18 \)
Now, sum all these results: \( 27+15 + 3+18=63 \)

Step1: Identify the region

The region for students taking chemistry and biology but not physics is the \( C\cap B \) only region.

Step2: Get the value

From the Venn diagram, the value of the \( C\cap B \) only region is 5.

Step1: Identify the region

The region of students not taking science is the region outside the three sets (chemistry, biology, physics) in the universal set.

Step2: Get the value

From the Venn diagram, the value of the region outside all three sets is 18.

Answer:

63

Second Question: How many students are taking chemistry and biology, but not physics?