Math  /  Discrete

QuestionPoints: 0 of 1 Save A middle school counselor, attempting to correlate school performance with leisure interests, found that of a group of students, 36 had seen Movie A, 29 had seen Movie B, 27 had seen Movie C, 17 had seen Movies A and B, 14 had seen Movies A and C, 10 had seen Movies B and C, 5 had seen all three films, and 6 had seen none of the three films. Use a Venn diagram to complete parts (a) through (c) below.
Complete the Venn diagram. Let AA be the set of students that saw Movie A,BA, B be the set of students that saw Movie B, and CC be the set of students that saw Movie CC. s=t=u=v=w=x=x=y=z=\begin{array}{l} \mathrm{s}=\square \\ \mathrm{t}=\square \\ \mathrm{u}=\square \\ \mathrm{v}=\square \\ \mathrm{w}=\square \\ \mathrm{x}=\square \\ \mathrm{x}=\square \\ \mathrm{y}=\square \\ \mathrm{z}=\square \end{array}

Studdy Solution
Fill in the values into the Venn diagram and verify the solution by summing all categories to match the total number of students.
\begin{align*} s &= 10 \\ t &= 7 \\ u &= 8 \\ v &= 12 \\ w &= 9 \\ x &= 5 \\ y &= 5 \\ z &= 6 \end{align*}
Verification: 10+7+8+12+9+5+5+6=6210 + 7 + 8 + 12 + 9 + 5 + 5 + 6 = 62
Thus, the total number of students is 62, which matches the sum of all categories.

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