Question

Soccer and track are two of several sports available for student participation at Roosevelt High School. Students who participate in at least one sport are asked to list all the sports in which they participate. Which Venn diagram shows a shaded sample space that represents students who are not participating in soccer and track?

Answer 1

To answer the question, the Venn diagram that shows a shaded sample space that represents students who are not participating in soccer and track would have two circles, one representing soccer and one representing track, that do not overlap. The area outside of the two circles would be shaded to represent the students who are not participating in soccer and track.

Answer 2

The correct answer is: C

To determine the Venn diagram that represents students who are not participating in soccer and track, we can use the principle of set theory. Let's denote the sets as follows:

• S: Set of students participating in soccer.
• T: Set of students participating in track.
• U: Universal set of all students.

The shaded sample space that represents students who are not participating in soccer and track is given by the complement of the union of sets S and T within the universal set U. The complement is denoted by S' ∩ T' or (S ∪ T)'.

1. Identify the sets:

• S: Soccer participants.
• T: Track participants.
• U: Universal set of all students.

Understand the complement:

• The complement of a set A is denoted by A' and represents all elements not in A.

Write the expression for students not participating in soccer and track:

• The students not participating in soccer and track can be represented as (S ∪ T)' or S' ∩ T'.

Draw the Venn diagram:

• Choose the Venn diagram option that correctly represents the complement (S ∪ T)' or S' ∩ T'.
• Given the options:
  A) Soccer and track no shaded - This option does not represent the complement.
  B) Soccer and track only common part is shaded - This option represents S ∩ T, not the complement.
  C) Soccer and track other than common part shaded - This option represents (S ∪ T)' or S' ∩ T'. It is a correct representation of students not participating in soccer and track.
  D) Soccer and track shaded is n(SOCCER) + n(TRACK) - n(soccer ∩ track) - This seems to be a mathematical expression and not a Venn diagram representation.

Therefore, the correct answer is: C) Soccer and track other than common part shaded.