Question

a venn diagram shows the memberships for the math, music, and science clubs. use the diagram to answer the questions below.
(a) select all the clubs that greg is not a member of. math music science
(b) how many students are members of the science club or the math club (or both)? students
(c) which of these students are in only one club? choose all that apply. greg mary dan ann chau ryan

Explanation:

(a)

Step1: Analyze Greg's membership

Greg is only in the Music club. So he is not in Math and Science.

(b)

Step1: List members of Science or Math (or both)

Members of Math: Ryan, Ann, Tom, Omar, Jane, Yoko, Chau
Members of Science: Jane, Yoko, Chau, Jose, Dan, Mary
Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)
\(n(\text{Math}) = 7\), \(n(\text{Science})=6\), \(n(\text{Math}\cap\text{Science}) = 3\) (Jane, Yoko, Chau)
\(n(\text{Math}\cup\text{Science})=7 + 6-3=10\)

(c)

Step1: Check each student

• Greg: only Music (not the clubs in question)
• Mary: only Science
• Dan: only Science
• Ann: only Math
• Chau: in Math, Music, Science (more than one)
• Ryan: only Math

Answer:

(a) Math, Science
(b) 10
(c) Mary, Dan, Ann, Ryan