$$A \times B = \{(orange, 1), (orange, 2), (banana, 1), (banana, 2), (apple, 1), (apple, 2)\}$$

$$B \times A = \{(1, orange), (1, banana), (1, apple), (2, orange), (2, banana), (2, apple)\}$$

$$A - B = \{x \mid x \in A \text{ and } x \notin B\}$$

Question 1

Given $$U = \{a, b, c, d, e, f, g\}$$ and $$A = \{a, c, e\}$$, what is the complement of $$A$$ ($$A'$$)?

Accepted Answer

$$A' = \{b, d, f, g\}$$

Question 2

If $$A = \{1, 2, 3, 8\}$$ and $$B = \{1, 3, 6, 7, 8\}$$, what is $$A \cap B$$?

Accepted Answer

$$A \cap B = \{1, 3, 8\}$$

Question 3

Which of the following best describes disjoint sets?

Accepted Answer

Two sets with no elements in common

Question 4

Given $$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$, $$A = \{1, 2, 4, 6\}$$, and $$B = \{1, 3, 6, 7, 9\}$$, what is $$A \cup B$$?

Accepted Answer

$$A \cup B = \{1, 2, 3, 4, 6, 7, 9\}$$

Question 5

If $$A = \{b, d, e, f, g, h\}$$ and $$B = \{a, b, d, h, i\}$$, what is $$A - B$$?

Accepted Answer

$$A - B = \{e, f, g\}$$

Question 6

A survey at a national park found that 25 visitors speak Spanish, 14 speak French, and 4 speak both. How many speak Spanish or French?

Accepted Answer

$$n(A \cup B) = 25 + 14 - 4 = 35$$

Question 7

Which region in a Venn diagram represents elements that are in both $$A$$ and $$B$$?

Accepted Answer

Region II

Question 8

If $$A = \{orange, banana, apple\}$$ and $$B = \{1, 2\}$$, what is $$A 	imes B$$?

Accepted Answer

$$A 	imes B = \{(orange, 1), (orange, 2), (banana, 1), (banana, 2), (apple, 1), (apple, 2)\}$$

Question 9

Which of the following is the correct formula for the number of elements in the union of two finite sets $$A$$ and $$B$$?

Accepted Answer

$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$

Question 10

If $$A = \{1, 2, 3, 8\}$$, $$B = \{1, 3, 6, 7, 8\}$$, and $$C = \{\}$$, what is $$A \cap C$$?

Accepted Answer

$$A \cap C = \{\}$$

Question 11

Which of the following statements is true about proper subsets?

Accepted Answer

If $$A is a $$proper subset of $$B$$, then every element of $$A is in$$ $$B$$ and $$A 
eq B$$

Question 12

Given $$U = \{a, b, c, d, e, f, g, h, i, j, k\}$$, $$A = \{b, d, e, f, g, h\}$$, $$C = \{b, e, g\}$$, what is $$A - C'$$?

Accepted Answer

$$A - C' = \{b, e, g\}$$

Question 13

Which of the following best describes the Cartesian product $$B 	imes A if$$ $$A = \{orange, banana, apple\}$$ and $$B = \{1, 2\}$$?

Accepted Answer

$$B 	imes A = \{(1, orange), (1, banana), (1, apple), (2, orange), (2, banana), (2, apple)\}$$

Question 14

If $$A = \{1, 2, 3, 8\}$$ and $$B = \{1, 3, 6, 7, 8\}$$, what is $$(A \cap B)' in$$ $$U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$$?

Accepted Answer

$$(A \cap B)' = \{2, 4, 5, 6, 7, 9, 10\}$$

Question 15

Which of the following is the set-builder notation for the difference $$A - B$$?

Accepted Answer

$$A - B = \{x \mid x \in A 	ext{ and } x 
otin B\}$$

Question 16

If $$A = \{1, 2, 4, 6\}$$ and $$C = \{\}$$, what is $$A \cup C$$?

Accepted Answer

$$A \cup C = \{1, 2, 4, 6\}$$

Question 17

Which of the following is true about the complement of a set $$A in $$universal set $$U$$?

Accepted Answer

It contains all elements in $$U$$ that are not in $$A$$

Venn Diagrams and Set Operations: Foundations for Intermediate Algebra

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