Deck 9: Geometry

Question 1

Decide whether the given set of numbers is a group under the given operation.
Rational numbers; multiplication

A) Yes
B) No

Answer 1

B

Question 2

Decide whether the given set of numbers is a group under the given operation.
Even integers; multiplication

A) Yes
B) No

Answer 2

B

Question 3

Decide whether the given set of numbers is a group under the given operation.
Rational numbers; multiplication

A) Yes
B) No

Answer 3

B

Question 4

Decide whether the given set of numbers is a group under the given operation.
Even integers; multiplication

A) Yes
B) No

Question 5

Decide whether the given set of numbers is a group under the given operation.
Natural numbers; addition

A) Yes
B) No

Question 6

Decide whether the given set of numbers is a group under the given operation.
Prime numbers; multiplication

A) Yes
B) No

Question 7

Decide whether the given set of numbers is a group under the given operation.
Integers; addition

A) Yes
B) No

Question 8

Decide whether the given set of numbers is a group under the given operation.
Whole numbers; multiplication

A) Yes
B) No

Question 9

Decide whether the given set of numbers is a group under the given operation.
Whole numbers; addition

A) No
B) Yes

Question 10

Decide whether the given set of numbers is a group under the given operation.
Whole numbers; multiplication

A) Yes
B) No

Question 11

Decide whether the given set of numbers is a group under the given operation.
Natural numbers; subtraction

A) Yes
B) No

Question 12

Decide whether the given set of numbers is a group under the given operation.
Even integers; addition

A) Yes
B) No

Question 13

Does the associative property hold for the set of real numbers under the operation of
subtraction? Support your claim with an example.

Question 14

Does the associative property hold for the set of real numbers under the operation of
division? Support your claim with an example.

Question 15

Decide whether the given set of numbers is a group under the given operation.
Prime numbers; multiplication

A) Yes
B) No

Question 16

Decide whether the given set of numbers is a group under the given operation.
Integers; addition

A) Yes
B) No

Question 17

Decide whether the given set of numbers is a group under the given operation.
Natural numbers; addition

A) Yes
B) No

Question 18

Decide whether the given set of numbers is a group under the given operation.
Natural numbers; subtraction

A) Yes
B) No

Question 19

Decide whether the given set of numbers is a group under the given operation.
Whole numbers; addition

A) Yes
B) No

Question 20

Decide whether the given set of numbers is a group under the given operation.
Even integers; addition

A) Yes
B) No

Question 21

Give the additive and multiplicative inverses of 6 for the set of rational numbers.

Question 22

Is there an identity element for the operation of division over the set of integers? Support
your claim with an example.

Question 23

Does the commutative property hold for the set of real numbers under the operation of
division? Support your claim with an example.

Question 24

Is the set of integers closed under the operation of subtraction? Support your claim with
an example.

Question 25

Determine the sum or difference in clock 12 arithmetic.
11 + 4

A) 4
B) 3
C) 7
D) 15

Question 26

Determine the sum or difference in clock 12 arithmetic.
4 - 9

A) 6
B) 0
C) 8
D) 7

Question 27

Does the commutative property hold for the set of real numbers under the operation of
subtraction? Support your claim with an example.

Question 28

Determine the sum or difference in clock 12 arithmetic.
(12 + 7) + 12

A) 31
B) 3
C) 8
D) 7

Question 29

Determine the sum or difference in clock 12 arithmetic.
2 - 9

A) 5
B) 4
C) 0
D) 3

Question 30

Is the set of integers closed under the operation of division? Support your claim with an
example.

Question 31

Determine the sum or difference in clock 12 arithmetic.
(7 + 10) + (12 + 9)

A) 8
B) 2
C) 1
D) 38

Question 32

Give the additive and multiplicative inverses of -2 for the set of rational numbers.

Question 33

Determine the sum or difference in the given clock arithmetic.
1 + 5 (clock 6)

A) 3
B) 6
C) 4
D) 1

Question 34

Determine the sum or difference in clock 12 arithmetic.
(2 + 1) + (1 + 8)

A) 12
B) 4
C) 2
D) 1

Question 35

Is there an identity element for the operation of subtraction over the set of integers?
Support your claim with an example.

Question 36

Determine the sum or difference in clock 12 arithmetic.
11 - 7

A) 7
B) 5
C) 4
D) 8

Question 37

Determine the sum or difference in clock 12 arithmetic.
(5 + 12) + 7

A) 10
B) 5
C) 12
D) 1

Question 38

Determine the sum or difference in the given clock arithmetic.
2 - 6 (clock 6)

A) 6
B) 2
C) 3
D) 1

Question 39

Determine the sum or difference in clock 12 arithmetic.
6 - 5

A) 3
B) 1
C) 7
D) 2

Question 40

Determine the sum or difference in clock 12 arithmetic.
10 + 2

A) 0
B) 24
C) undefined
D) 12

Question 41

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

A) Closure, identity, and inverse only
B) All of them
C) Closure, identity, inverse, and commutative only
D) Closure, identity, associative, and commutative only

Question 42

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { c | c c c c } ?? & 2 & 8 & 11 & 16 \\ \hline 2 & 8 & 11 & 16 & 2 \\8 & 11 & 16 & 2 & 8 \\11 & 16 & 2 & 8 & 11 \\16 & 2 & 16 & 11 & 8\end{array}$$

A) Closure, identity, and inverse only
B) Closure only
C) Closure, identity, inverse, and commutative only
D) All of them

Question 43

Determine the sum or difference in the given clock arithmetic.
2 + (4 - 5) (clock 6)

A) 4
B) 2
C) 1
D) 3

Question 44

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

A) Closure, identity, and commutative only
B) Closure, identity, inverse, and associative only
C) Closure, identity, associative, and commutative only
D) None of them

Question 45

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { l | l l l } ? & \wedge & £ & \Phi \\\hline \wedge & \wedge & £ & \Phi \\£ & £ & \wedge & \Phi \\\Phi & \Phi & £ & \wedge\end{array}$$

A) Closure, identity, inverse, and associative only
B) Closure, identity, and inverse only
C) All of them
D) Closure only

Question 46

Solve the problem.
If May is your starting month, what month will it be 36 months from May?

A) April
B) June
C) May
D) October

Question 47

Determine the sum or difference in the given clock arithmetic.
(1 - 6) - 2 (clock 7)

A) 1
B) 7
C) 5
D) 3

Question 48

Determine the sum or difference in the given clock arithmetic.
2 + 5 (clock 7)

A) 5
B) 7
C) 1
D) 2

Question 49

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

A) All of them
B) None of them
C) Closure, identity, inverse, and commutative only
D) Closure, identity, inverse, and associative only

Question 50

Solve the problem.
If October is your starting month, what month will it be 18 months from October?

A) January
B) May
C) April
D) August

Question 51

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

A) Closure and identity only
B) Closure, identity, and inverse only
C) Closure only
D) Closure, identity, inverse, and associative only

Question 52

Determine the sum or difference in the given clock arithmetic.
(3 - 4) - 6 (clock 6)

A) 5
B) 2
C) 6
D) 3

Question 53

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { c | c c c c } ‡ & 4 & 9 & 14 & 19 \\ \hline 4 & 14 & 19 & 4 & 9 \\9 & 19 & 4 & 9 & 14 \\14 & 4 & 9 & 14 & 19 \\19 & 9 & 14 & 19 & 4\end{array}$$

A) Closure, identity, inverse, and commutative only
B) Closure, identity, associative, and commutative only
C) Closure, identity, inverse, and associative only
D) All of them

Question 54

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { c | c c c } ? & 3 & 8 & 11 \\ \hline 3 & 8 & 11 & 3 \\8 & 11 & 3 & 8 \\11 & 3 & 8 & 11\end{array}$$

A) All of them
B) Closure, identity, inverse, and associative only
C) Closure, identity, associative, and commutative only
D) Identity, inverse, and commutative only

Question 55

Determine the sum or difference in the given clock arithmetic.
2 + (4 - 4) (clock 7)

A) 5
B) 4
C) 3
D) 2

Question 56

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { c | c c c } ? & \vee & ¥ & \Theta \\\hline \vee & \vee & \Theta & ¥ \\¥ & \Theta & ¥ & \vee \\\Theta & ¥ &£ & \vee \end{array}$$

A) None of them
B) Closure only
C) Closure, identity, associative, and commutative only
D) Closure, identity, inverse, and associative only

Question 57

Determine the sum or difference in the given clock arithmetic.
1 - 6 (clock 7)

A) 4
B) 3
C) 5
D) 2

Question 58

Determine the sum or difference in the given clock arithmetic.
4 - 3 (clock 7)

A) 3
B) 1
C) 5
D) 2

Question 59

Decide which of the 5 properties of a commutative group (closure, identity, inverse, associative, commutative) hold for
the given system.

- $$\begin{array} { c | c c c c } / & 5 & 11 & 16 & 8 \\\hline 5 & 11 & 16 & 8 & 5 \\11 & 16 & 8 & 5 & 11 \\16 & 8 & 5 & 11 & 16 \\8 & 5 & 11 & 16 & 8\end{array}$$

A) Closure, identity, associative, and commutative only
B) All of them
C) Closure, identity, inverse, and commutative only
D) Closure, identity, inverse, and associative only

Question 60

Determine the sum or difference in the given clock arithmetic.
5 - 3 (clock 6)

A) 5
B) 1
C) 6
D) 2

Question 61

Perform the modular arithmetic operation.
9 ∙ 9 (mod 7)

A) 3
B) 7
C) 11
D) 4

Question 62

Perform the modular arithmetic operation.
42 - 29 (mod 4)

A) 0
B) 52
C) 1
D) 2

Question 63

Solve the problem.
If Sunday is your starting day, what day will it be 1 year, 43 days from Sunday? (Assume no leap
Years.)

A) Thursday
B) Tuesday
C) Friday
D) Sunday

Question 64

Perform the modular arithmetic operation.
[(9 ∙ 7) - 1] (mod 5)

A) 1
B) 2
C) 3
D) 4

Question 65

Perform the modular arithmetic operation.
10 + 13 (mod 8)

A) 2
B) 6
C) 7
D) 8

Question 66

Find the modulo class to which the number belongs for the given modulo system.
69, mod 16

A) 5
B) 13
C) 10
D) 8

Question 67

Find the modulo class to which the number belongs for the given modulo system.
57, mod 13

A) 9
B) 1
C) 5
D) 12

Question 68

Perform the modular arithmetic operation.
[(11 ∙ 4) + 4] (mod 8)

A) 7
B) 1
C) 0
D) 3

Question 69

Perform the modular arithmetic operation.
19 - 54 (mod 6)

A) 1
B) 0
C) 210
D) 4

Question 70

Solve the problem.
If Saturday is your starting day, what day will it be 34 days from Saturday?

A) Saturday
B) Thursday
C) Sunday
D) Friday

Question 71

Solve the problem.
If Wednesday is your starting day, what day will it be 156 days from Wednesday?

A) Wednesday
B) Thursday
C) Saturday
D) Friday

Question 72

Solve the problem.
If May is your starting month, what month will it be 73 months from May?

A) April
B) June
C) December
D) March

Question 73

Perform the modular arithmetic operation.
[(5 - 7) ∙ 7] (mod 5)

A) 4
B) 1
C) 0
D) 3

Question 74

Solve the problem.
If April is your starting month, what month will it be 5 years and 2 months from April?

A) August
B) June
C) October
D) May

Question 75

Perform the modular arithmetic operation.
124 + 125 (mod 12)

A) 9
B) 13
C) 8
D) 20

Question 76

Find the modulo class to which the number belongs for the given modulo system.
21, mod 8

A) 2
B) 7
C) 5
D) 1

Question 77

Find the modulo class to which the number belongs for the given modulo system.
13, mod 4

A) 3
B) 0
C) 2
D) 1

Question 78

Solve the problem.
If Thursday is your starting day, what day will it be 2 years, 24 days from Thursday? (Assume no
Leap years.)

A) Friday
B) Wednesday
C) Thursday
D) Tuesday

Question 79

Solve the problem.
If November is your starting month, what month will it be 16 years from November?

A) July
B) March
C) November
D) April

Question 80

Solve the problem.
If Tuesday is your starting day, what day will it be 3 years, 348 days from Tuesday? (Assume no
Leap years.)

A) Tuesday
B) Monday
C) Sunday
D) Wednesday