Question 1

Which of the following best describes the empty set?

Accepted Answer

A set that contains no elements at all.

Question 2

Let $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}. $$What is $$A \cup B$$?

Accepted Answer

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

Question 3

If $$U is $$the universal set and $$A is $$any subset of $$U$$, which of the following is always true?

Accepted Answer

$$A \subseteq U$$

Question 4

Given $$A = \{	ext{fish}, 	ext{cat}\}$$ and $$B = \{	ext{fish}, 	ext{cat}, 	ext{dog}\}$$, which statement is correct?

Accepted Answer

$$A \subseteq B$$

Question 5

Which of the following is the correct definition of the intersection of two sets $$A$$ and $$B$$?

Accepted Answer

The set of all elements that are in both $$A$$ and $$B.$$

Question 6

Let $$U = \{1, 2, 3, 4, 5\}$$ and $$A = \{2, 4\}. $$What is the complement of $$A in$$ $$U$$, denoted $$A^c$$?

Accepted Answer

$$\{1, 3, 5\}$$

Question 7

Suppose $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{3\}$$

Question 8

If $$A = \emptyset$$ and $$B = \{1, 2\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2\}$$

Question 9

Which of the following statements about subsets is always true?

Accepted Answer

$$\emptyset \subseteq A$$ for any set $$A$$

Question 10

Let $$A = \{1, 2, 3, 4\}$$ and $$B = \{3, 4, 5, 6\}. $$How many elements are in $$A \cup B$$?

Accepted Answer

6

Question 11

If $$n(A) = 10$$, $$n(B) = 15$$, and $$n(A \cap B) = 5$$, what is $$n(A \cup B)$$?

Accepted Answer

20

Question 12

A hospital study records patients who received therapy A, therapy B, or both. If 30 patients received therapy A, 25 received therapy B, and 10 received both, how many patients received at least one therapy?

Accepted Answer

45

Question 13

Which of the following is a correct symbolic representation for 'x is an element of set Q'?

Accepted Answer

$$x \in Q$$

Question 14

Let $$A = \{	ext{Ontario}, 	ext{Alberta}, 	ext{BC}\}$$ and $$B = \{	ext{Ontario}, 	ext{Quebec}\}. $$What is $$A \cap B$$?

Accepted Answer

$$\{	ext{Ontario}\}$$

Question 15

If $$A = \{1, 2, 3\}$$ and $$B = \{4, 5, 6\}$$, what is $$A \cap B$$?

Accepted Answer

$$\emptyset$$

Question 16

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

Accepted Answer

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

Question 17

Suppose $$U = \{1, 2, 3, 4, 5, 6\}$$ and $$A = \{2, 4, 6\}. $$What is $$A^c$$?

Accepted Answer

$$\{1, 3, 5\}$$

Question 18

If $$A = \{	ext{cat}, 	ext{dog}\}$$ and $$B = \{	ext{fish}, 	ext{cat}, 	ext{dog}\}$$, which of the following is true?

Accepted Answer

$$A \subseteq B$$

Question 19

A survey of 100 people found that 60 like tea, 50 like coffee, and 20 like both. How many people like neither tea nor coffee?

Accepted Answer

10

Fundamentals of Sets in Statistics

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