Question 1

Given the universal set $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$ and the sets $$A = \{1, 2, 3, 4, 5\}$$, $$B = \{0, 2, 4, 6, 8\}$$, and $$C = \{2, 3, 5, 7, 8\}$$, what is $$A \cap B \cap C$$?

Accepted Answer

$$\{2\}$$

Question 2

Using the same sets as above, what is $$A \cup (B \cap C)$$?

Accepted Answer

$$\{0, 1, 2, 3, 4, 5, 8\}$$

Question 3

Which region(s) in the Venn diagram represent $$(B \cup C) \cap A'$$?

Accepted Answer

$$\{0, 6, 7, 8\}$$

Question 4

Given $$U = \{1, 2, 3, \ldots, 20\}$$, $$E = \{2, 4, 6, \ldots, 20\}$$, $$F = \{5, 10, 15, 20\}$$, $$G = \{1, 2, 3, 4, 5\}$$, what is $$(E \cup F \cup G)'$$?

Accepted Answer

$$\{6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19\}$$

Question 5

Which of the following is equivalent to $$(B \cap A') \cup (C \cap A')$$?

Accepted Answer

$$(B \cup C) \cap A'$$

Question 6

If $$A = \{1, 2, 3, 4, 5\}$$, $$B = \{0, 2, 4, 6, 8\}$$, $$C = \{2, 3, 5, 7, 8\}$$, what is $$(A \cup B \cup C)'$$?

Accepted Answer

$$\{6, 9\}$$

Question 7

Given $$A = \{1, 2, 3, 4, 5\}$$, $$B = \{0, 2, 4, 6, 8\}$$, $$C = \{2, 3, 5, 7, 8\}$$, what is $$A' \cap B' \cap C'$$?

Accepted Answer

$$\{6, 9\}$$

Question 8

Which of the following best describes $$(A \cap B) \cup (B \cap C) \cup (C \cap A)$$?

Accepted Answer

$$\{2, 3, 4, 5, 8\}$$

Question 9

If $$E = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}$$, $$F = \{5, 10, 15, 20\}$$, $$G = \{1, 2, 3, 4, 5\}$$, what is $$(E \cup F) \cap (F \cup G)$$?

Accepted Answer

$$\{2, 4, 5, 10, 15, 20\}$$

Question 10

Given $$F = \{5, 10, 15, 20\}$$, $$E = \{2, 4, 6, 8, 10, 12, 14, 16, 18, 20\}$$, $$G = \{1, 2, 3, 4, 5\}$$, what is $$F' \cap (E \cup G') in$$ $$U = \{1, 2, 3, ..., 20\}$$?

Accepted Answer

$$\{6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19\}$$

Question 11

Which of the following is the result of $$(E \cap F') \cup (G' \cap F')$$?

Accepted Answer

$$\{2, 4, 6, 8, 12, 14, 16, 18, 1, 3, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19\}$$

Question 12

If you shade the region representing $$(B \cap A') \cup (C \cap A') on a $$Venn diagram, which elements are included?

Accepted Answer

$$\{0, 6, 7, 8\}$$

Question 13

Which of the following is a true statement about the relationship between $$(B \cup C) \cap A'$$ and $$(B \cap A') \cup (C \cap A')$$?

Accepted Answer

They are equivalent sets.

Question 14

Given the Venn diagram, which set operation would result in the set $$\{2, 3, 4, 5, 8\}$$?

Accepted Answer

$$(A \cap B) \cup (B \cap C) \cup (C \cap A)$$

Question 15

If $$A = \{1, 2, 3, 4, 5\}$$, $$B = \{0, 2, 4, 6, 8\}$$, $$C = \{2, 3, 5, 7, 8\}$$, what is $$A \cap (B \cup C)$$?

Accepted Answer

$$\{2, 3, 4, 5\}$$

Question 16

Which of the following is the complement of $$A \cup B \cup C in$$ $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$?

Accepted Answer

$$\{6, 9\}$$

Venn Diagrams & Operations with Three Sets – Study Guidance

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