Multiple Choice
Identify the choice that best
completes the statement or answers the question.
|
|
|
1.
|
Which statement is false?
A. | Trigonometry is a subset of mathematics. | B. | The cities in
Manitoba are a subset of the cities in Canada. | C. | Squashes are a subset of
vegetables. | D. | Birds are a subset of mammals. |
|
|
|
2.
|
Which pair of sets represents one set being a subset of another but is not
equal?
A. | N, the set of natural numbers, and I, the set of
integers | B. | T, the set of all triangles, and C, the set of all
circles | C. | N, the set of natural numbers, and P, the set of positive
integers | D. | none of the above |
|
|
|
3.
|
Given the following situation:
• the universal set U = {positive
integers less than 20}
• X = {4, 5, 6, 7, 8}
• P = {prime numbers of
U}
• O = {odd numbers of U}
Which is the complement of
P?
A. | the even numbers of U | B. | the universal set excluding the set of
X | C. | the positive integers greater than 20 | D. | the non-prime numbers of
U |
|
|
|
4.
|
A summer camp offers canoeing, rock climbing, and archery. The following Venn
diagram shows the types of activities the campers like.  Use the diagram to
determine n(( A Ç C) È ( R Ç A)).
|
|
|
5.
|
Some table games use a board, dice, or cards, or a combination these. The
following Venn diagram shows the number of games that use these tools.  Use
the diagram to determine n( B \ D) ¢.
|
|
|
6.
|
Which sentence is written as a conditional statement?
A. | If you fall down, get right back up. | B. | Juggling is not hard if you
practice. | C. | If the temperature is below freezing, it must be winter. | D. | If the sky is
cloudy, then you cannot see the sun. |
|
|
|
7.
|
Which sentence is the converse to the conditional statement below?
“If
students are in school, then it is a weekday.”
A. | If it is a weekday, then students are in school. | B. | If it is not a
weekday, then students are not in school. | C. | During the week, students are in
school. | D. | Students go to school on weekdays. |
|
|
|
8.
|
Which conditional statement is false?
A. | 12 o’clock is midnight if and only if it is not noon. | B. | It is real maple
syrup if and only if the syrup is made from maple sap. | C. | It is Valentine’s Day if and only if it
is February 14. | D. | It is a whale if and only if is it a mammal that lives in the
ocean. |
|
|
|
9.
|
What is the inverse?
A. | a conditional statement in which the hypothesis and the conclusion are
switched | B. | a statement that is formed by negating both the hypothesis and the conclusion of a
conditional statement | C. | a statement that is formed by negating both the
hypothesis and the conclusion of the converse of a conditional statement | D. | a statement that is
formed by inverting both the hypothesis and the conclusion of a conditional
statement |
|
|
|
10.
|
What is true about the conditional statement below?
“If tomorrow is
Monday, then today is Sunday.”
A. | The statement and contrapositive are true but the inverse and converse are
false. | B. | The inverse and contrapositive are true but the statement and converse are
false. | C. | The converse and inverse are true but statement and contrapositive are
false. | D. | The statement, converse, inverse, and contrapositive are all true.
|
|
Short Answer
|
|
|
1.
|
What is the set notation for the set of all natural numbers greater than
1 and less than or equal to 50?
|
|
|
2.
|
The city surveyed 3000 people about how they travel to work.
• 1978
took public transit (P)
• 1494 drove (D)
• 818 cycled
(C)
• 731 took public transit and drove only
• 298 took public transit and
cycled only
• 27 drove and cycled only
• 164 used all three modes of
transportation
How many people cycle but do not drive? Write your answer using set
notation.
|
|
|
3.
|
Show the biconditional statement below is true. If it is not true, give a
counterexample.
“You are in the capital city of Canada if and only if you are in
Ontario.”
|
Problem
|
|
|
1.
|
Consider this universal set:
A = {A, B, C, D, E, F, G, H, I, J, K, L,
M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z}
a) List the following subsets:
•
C = {letters that are consonants}
• V = {letters that are vowels}
b)
Represent the universal set and subsets in a Venn diagram.
c) Are C and
V are disjoints sets? Explain.
|
|
|
2.
|
A total of 83 teens attended a performing arts camp to train in at least one of
three activities: dance, acting, or singing.
• 47 took dance, 42 took acting, and 54 took
singing.
• 3 took dance and acting only.
• 16 took acting and singing
only.
• 19 took dance and singing only.
How many teens trained in all three performing
arts?
|