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)'.
- 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.