# 2.5: Homework

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• Submit homework separately from this workbook and staple all pages together. (One staple for the entire submission of all the unit homework)
• Start a new module on the front side of a new page and write the module number on the top center of the page.
• Some solutions are given in the solutions manual.
• You may work with classmates but do your own work.
##### Hw #1

Let U = {a, c, e, m n, r, u, v, w, x, z} with subsets A, B, C and D defined below: A = {m, n, r, u, x} B = { a, c , r, u, x} C = {e, v, w, x, z } D = {a, c, z} Using correct notation, find the following, show all work

 a. $$\bf B \cap D$$ f. $$\bf A - C^{c}$$ k. $$\bf (A \cap D) - B^{c}$$ b. $$\bf A \cap D$$ g. $$\bf B - (A \cap C)$$ l. n($$\bf A \cup B$$) c. C - B h. $$\bf D^{c} - (B \cup C)$$ m. n(A) + n(B) d. $$\bf (A \cup C)^{c}$$ i. $$\bf (A \cap B) \cap (C \cup D)$$ n. n(D - C) e. $$\bf D^{c} \cap B$$ j. $$\bf (B^{c} \cup D)^{c}$$ o. n($$\bf B \cap C$$)
##### HW #2

Let U = {a, c, e, m n, r, u, v, w, x, z} with subsets A, B, C defined as follows:

 A = {m, n, r, u, v} B = {r, u, w, x} C = {n, r, x, c}

Draw a Venn Diagram and place each element of the universe in the correct region

##### HW #3

Use deMorgan's Laws to rewrite each of the following:

 a. $$\bf N \cup P^{c}$$ b. $$\bf R^{c} \cap S$$
##### HW #4

Use the distributive properties of sets to rewrite each of the following:

 a. $$\bf (A^{c} \cup E) \cap (A^{c} \cup F)$$ b. $$\bf B \cap (A \cup C)$$
##### HW #5

A survey was given to determine which of the three beverages (tea, milk and/or coffee) people drank each day. The results were as follows:

 7 only drank coffee 6 drank all three 11 drank tea and coffee 21 drank coffee 4 drank none of the three 9 drank neither coffee or tea 21 drank tea 1 drank only tea and milk
 a. Draw a Venn diagram indicating how many people would belong in each region. Label the three sets with meaningful letters. b. How many people were surveyed? c. How many drank milk? d. How many drank only coffee and milk? e. How many drank only milk? f. How many drank tea or coffee but not milk? g. How many drank exactly two kinds of beverages? h. How many didn’t drink milk or tea?
##### HW #6

Take out your A–blocks and arrange them into subsets so that each subset only contains elements that have the same size and color.

 a. How many subsets are there? b. How many pieces are in each subset?
##### HW #7

Let A, B and C represent any sets. Answer True or False for the following statements. In order for a statement to be true, it must always be true. For each False statement, give an example of why it is False.

 a. B is always a subset of $$\bf A \cup B$$ b. $$\bf (A - B)^{c} = A^{c} - B^{c}$$ c. B is always a subset of $$\bf A \cap B$$ d. $$n$$($$\bf A \cup B$$) = $$n$$(A) + $$n$$(B) e. $$n$$($$\bf A \cup B)$$ = $$n$$(A) + $$n$$(B) – $$n$$($$\bf A \cap B$$) f. If $$n$$($$\bf A \cup B$$) = $$n$$(A) + $$n$$(B), then A and B are disjoint.
##### HW #8

Draw a Venn diagram and shade in the region that represents the following

 a. $$\bf (C \cup A) - B$$ b. $$\bf (C \cap B) \cup A$$ c. $$\bf (C \cap B) - A$$ d. $$\bf (A \cup C) \cap B$$ e. $$\bf \bar{A} - (B \cap C)$$ f. $$\bf (B - A) \cap (B - C)$$
##### HW #9

Identify the shaded area of each Venn diagram by set notation.

 a. b.
##### HW #10

List all possible subsets for each set given.

 a. { } b. {a} c. {a, b} d. {a, b, c}
##### HW #11

Let A = {1, 2, 4}, B = {(a, c), 5} and C = {x}. Find the following:

 a. $$A \times A$$ a. $$A \times B$$ c. $$B \times C$$ d. $$C \times A$$ a. $$C \times C$$
##### HW #12

Use your A–blocks to do this problem. Let X represent the set of large circles and Y represent the set of red circles. Using set notation and abbreviations, find the following:

 a. X - Y b. $$\bf X \cap Y$$ c. $$\bf X \cup Y$$ d. Y - X

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