Good 1 Steve so I sux at math but your here :) Heres another:
X = [students playing football], Y = [students playing baseball], and Z = [students playing rugby]. Draw a Venn diagram of Z – (X U Y), and write a sentence describing what the set represents:
this is bogus. Maybe X,Y,Z are all disjoint. So, Z – (X U Y) = Z
maybe Z⊆(XUY) so Z – (X U Y) = Ø
Looks like you're on your own for this one.
To draw the Venn diagram of Z - (X U Y), we need to first understand the individual sets involved.
X represents the set of students playing football,
Y represents the set of students playing baseball, and
Z represents the set of students playing rugby.
To find Z - (X U Y), we have to subtract the union of X and Y from Z. Here's the step-by-step process to create the Venn diagram:
1. Draw a rectangle to represent the universal set, which in this case is all the students.
2. Draw three overlapping circles within the rectangle to represent X, Y, and Z.
3. Label the regions accordingly:
- The region inside circle X represents students playing football.
- The region inside circle Y represents students playing baseball.
- The region inside circle Z represents students playing rugby.
4. Determine the shared regions:
- The region where circles X and Z overlap represents students playing both football and rugby.
- The region where circles Y and Z overlap represents students playing both baseball and rugby.
5. Now, it's time to calculate Z - (X U Y). This means we are excluding the students playing football or baseball from the students playing rugby.
- Start by shading the entire region inside circle Z.
- Next, remove the regions where circles X and Y overlap (students playing both football and baseball). Leave these areas unshaded.
- Finally, what remains shaded inside circle Z represents the students playing only rugby, excluding football and baseball players.
In terms of the sentence describing the set Z - (X U Y), it represents the students who exclusively play rugby, not participating in either football or baseball.