Set Theory Review: Lesson 1-31. Let U be the universal set, with X⊂U .Determine n (X ) if n(U ) = 96 and n(X’ ) = 42.

2. Let Y = { even numbers between 20 and 40, inclusive}a) Determine n(Y).

b) P is a subset of Y where the elements are at most 28. List the elements of P.

c) List the elements of P’.

3. In each of the following Venn diagrams, shade the region indicated.

a) A∪B b) A ¿

U U

c) (A∩C)¿ d) U ¿

U

U

1

B

C

A

B

C

A B

C

A

B

C

A

4. Use the following sets:The universal set: U ={ natural numbers from 11 to 27 inclusive}Subsets: E={multiples of 3}

F = {multiples of 7} S = {multiples of 9}

a) Draw the Venn diagram.

b) List any pairs of disjoint subsets.

5. At a fitness centre, 80 people were working out. Set A contains 50 people that exercised with weights and Set B contains the 35 people that used the treadmill.

a) Draw the Venn diagram.

b) Determine n(A∪B)

c) Determine n(A∩B)

d) Determine n(A¿)

e) Determine n(B ¿)

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6. One of the great things about Canada is seeing many different cultures in one place. 205 people were asked if they celebrate Christmas, Hanukkah, or Kwanzaa. The results were as follows:

50 respondents don’t celebrate any of the three given observances. 80 people celebrate Christmas. 50 people celebrate Hanukkah. 60 people celebrate Kwanzaa. 15 people celebrate only Christmas and Hanukkah. 10 people celebrate only Christmas and Kwanzaa. 5 people celebrate all 3.

a) Draw a Venn diagram to represent this situation. Fill the correct number of people into each region of the Venn diagram.

b) What percentage of respondents celebrate only one of the given observances?

c) One region of the Venn diagram is empty. What does this represent?

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