Free Printable MATH 170 A Quiz

1.

Which of the following represents the set {x ∈ ℝ | x < 1 or x ≥ 4}?

a)

ℝ ∩ (1,4)

b)

ℝ ∩ [1,4)

c)

ℝ - [1,4]

d)

ℝ - (1,4)

2.

Let X = {1,2,3,4,5,6,7,8} and Y = {1,6,7,8}. Which of the following represents the set X - Y?

a)

ℕ - [2, 5]

b)

ℕ - (2, 5)

c)

ℕ ∩ (2, 5)

d)

ℕ ∪ (2,5)

3.

Find the truth values of p and q that will make the statement p ↔ (p̃ ∧ q) true.

a)

𝑝 = True , 𝑞 = True

b)

𝑝 = True , 𝑞 = False

c)

𝑝 = False , 𝑞 = True

d)

𝑝 = False , 𝑞 = False

e)

t’s not possible for the statement to be true

4.

What truth values of p and q would prove that propositions M and V are not logically equivalent? M: (p̃ ∧ q) → (p ∨ q) V: p ∨ q̃

a)

𝑝 = True , 𝑞 = True

b)

𝑝 = True , 𝑞 = False

c)

𝑝 = False , 𝑞 = True

d)

𝑝 = False , 𝑞 = False

5.

Find the truth value of these two statements if p is True and q is False: Statement #1: ¬p ∨ q Statement #2: (p ∧ q) → (p ∨ q)

a)

both statements are true

b)

both statements are false

c)

statement #1 is true, statement #2 is false

d)

statement #1 is false, statement #2 is true

6.

Let X be a subset of Y. Find the truth value of these two statements: Statement #1: X ∪ Y = Y Statement #2: X – Y = Ø

a)

both statements are true

b)

both statements are false

c)

statement #1 is true, statement #2 is false

d)

statement #1 is false, statement #2 is true

7.

Find the truth value of these two statements: Statement #1: (2,3) ∈ [1,4] Statement #2: [2,3] ∩ [3,8] = Ø

a)

both statements are true

b)

both statements are false

c)

statement #1 is true, statement #2 is false

d)

statement #1 is false, statement #2 is true

8.

Find the truth value of these two statements: Statement #1: ∀x ∈ Z(x² ≥ x) Statement #2: ∃x ∈ ℝ⁺(x – 2 < 0)

a)

both statements are true

b)

both statements are false

c)

statement #1 is true, statement #2 is false

d)

statement #1 is false, statement #2 is true

9.

Find the truth value of these two statements: Statement #1: ∀x ∈ ℝ(x^3 > 0) Statement #2: ∃x ∈ ℤ(x^2 - 2 = 0)

a)

both statements are true

b)

both statements are false

c)

statement #1 is true, statement #2 is false

d)

statement #1 is false, statement #2 is true

10.

Which of the following represents the set Z ∩ [-2, 3]?

(a)

11.

Which of the following represents the set {x ∈ ℝ | 2 ≤ x ≤ 5}?

(a)

12.

Which of the following represents the set [1,7) - (5,8]?

a)

{𝑥 ∈ ℝ | 1 ≤ 𝑥 ≤ 5}

b)

{𝑥 ∈ ℝ | 1 < 𝑥 ≤ 5}

c)

𝑥 ∈ ℝ | 1 ≤ 𝑥 < 5}

d)

{𝑥 ∈ ℝ | 1 < 𝑥 < 5}

13.

Let X = {a, b, c, d} and Y = {b, c, e, f, g, h, i}. How many elements are in the set Y - (X ∩ Y)?

(a)

14.

Choose the statement that is the negation of $ (x \land y) \lor z $.

a)

$ (x \land \lnot y) \land \lnot z $

b)

$ (x \land y) \lor \lnot z $

c)

$ (x \lor y) \land \lnot z $

d)

$ (x \lor y) \lor \lnot z $

e)

$ (x \land \lnot y) \lor \lnot z $

15.

Choose the statement that is equivalent to $ (x \land y) \lor z $.

a)

$ (x \lor \lnot y) \rightarrow z $

b)

$ (x \lor y) \lor z $

c)

$ (x \lor y) \rightarrow \lnot z $

d)

$ (x \lor \lnot y) \rightarrow \lnot z $

e)

$ (x \lor y) \rightarrow z $

16.

Choose the statement that is equivalent to: "4 < 7 unless today is Tuesday."

a)

If today is Tuesday, then 4 < 7.

b)

If today is Tuesday, then 4 ≥ 7.

c)

If today is not Tuesday, then 4 < 7.

d)

If today is not Tuesday, then 4 ≥ 7.

17.

Choose the statement that is the contrapositive of: "If the eraser is red or blue, then it is mine."

a)

If the eraser is mine, then it is not red and not blue.

b)

If the eraser is not mine, then it is not red and not blue.

c)

If the eraser is not mine, then it is red or blue.

d)

If the eraser is mine, then it is red but not blue.

e)

If the eraser is mine, then it is not red or not blue.

18.

Choose the statement that is the negation of: ( q → (p ∨ q) )

a)

( p ∨ ¬ q )

b)

( p ∨ q )

c)

( p → ¬ q )

d)

( p → q )

e)

( p ∧ ¬ q )

19.

The proposition ( (p → q) ∧ (p ∧ q) ) is a...

a)

contingency

b)

contradiction

c)

tautology

20.

Choose the statement that is equivalent to: "If the car is blue, then it has windows."

a)

The car is blue or it has no windows.

b)

The car is not blue or it has no windows.

c)

The car is blue or it has windows.

d)

The car is not blue or it has windows.

21.

Choose the statement that is equivalent to: "If 2 = 3, then I do not have a penny."

a)

I do not have a penny or 2 = 3.

b)

If I have a penny, then 2 ≠ 3.

c)

2 = 3 and I have a penny.

d)

I have a penny or 2 ≠ 3.

e)

If 2 ≠ 3, then I have a penny.

22.

Find the inverse of: “The book is heavy only if it’s my art book.”

a)

The book is not heavy implies that it’s not my art book.

b)

If it’s not my art book, then it is not heavy.

c)

The book is heavy or it’s my art book

d)

The book is not heavy when it’s my art book.

23.

Choose the converse of the statement: “The jar is broken if it was dropped.”

a)

If the jar is not broken, then it was dropped.

b)

If the jar is broken, then it was not dropped.

c)

If the jar is not broken, then it was not dropped.

d)

The jar is broken and it was not dropped

e)

If the jar is broken, then it was dropped.

24.

Thirty college students were asked if they are taking a math or history class, and the results are: 9 are taking math but not history, 4 are taking history but not math, 7 are taking both math and history, and 10 are taking neither. Let ( M ) represent the set of people who have a math class, and let ( H ) represent the set of people who have a history class. Find the following: |M ∪ H| = (a)

25.

Thirty college students were asked if they are taking a math or history class, and the results are: 9 are taking math but not history, 4 are taking history but not math, 7 are taking both math and history, and 10 are taking neither. Let ( M ) represent the set of people who have a math class, and let ( H ) represent the set of people who have a history class. Find the following: |M u H|' = (a)

26.

Thirty college students were asked if they are taking a math or history class, and the results are: 9 are taking math but not history, 4 are taking history but not math, 7 are taking both math and history, and 10 are taking neither. Let ( M ) represent the set of people who have a math class, and let ( H ) represent the set of people who have a history class. Find the following: |M' ∩ H| = (a)

27.

Thirty college students were asked if they are taking a math or history class, and the results are: 9 are taking math but not history, 4 are taking history but not math, 7 are taking both math and history, and 10 are taking neither. Let ( M ) represent the set of people who have a math class, and let ( H ) represent the set of people who have a history class. Find the following: |M - H| = (a)

28.

Which of the following is the contrapositive of: "If it rains, then the ground is wet."?

a)

If the ground is not wet, then it does not rain.

b)

If the ground is wet, then it rains.

c)

If it does not rain, then the ground is not wet.

d)

If it does not rain, then the ground is wet.

29.

Find the converse of the statement: "You can enter the club if you are over 21."

a)

If you are over 21, then you can enter the club.

b)

If you can enter the club, then you are over 21.

c)

If you are not over 21, then you cannot enter the club.

d)

If you cannot enter the club, then you are not over 21.

30.

Choose the statement that is equivalent to: "All roses are flowers."

a)

If it is a rose, then it is a flower.

b)

If it is not a rose, then it is not a flower.

c)

If it is a flower, then it is a rose.

d)

If it is not a flower, then it is not a rose.

31.

Suppose a function has a domain of {1, 2, 3, 4 } and a codomain of { 0, 1, 2, 3, 4 }. Which one of the
following is true?

a)

It cannot be onto

b)

It is must be onto

c)

It must be one to one

d)

It cannot one to one

32.

The function 𝑓(𝑥) = √𝑥 + 4 , where the domain is ℝ+, would be onto if the codomain were...

a)

(0,oo)

b)

(1,oo)

c)

(2,oo)

d)

(4,oo)

33.

In a group of 154 people, each person is asked to choose one favorite color from among blue, red,
yellow, or green. How many times must some color get selected?

(a)

34.

Find the inverse of the function. 𝑓: [2,8] → [7,16] , $f\left(x\right)=\left\{x+5\ if\ 2\le x<5,\ 2x\ if\ 5\le x\le8\right\}$

(a)

35.

Find the inverse of the function. 𝑓: [2,8] → [7,16] , $f\left(x\right)=\left\{x+5\ if\ 2\le x<5,\ 2x\ if\ 5\le x\le8\right\}$

a)

f^(-1)(x) = { x - 5 if 7 ≤ x < 10, x/2 if 10 ≤ x ≤ 16}

b)

f^(-1)(x) = { x - 5 if 7 ≤ x < 10, x + 2 if 10 ≤ x ≤ 16}

c)

f^(-1)(x) = { x + 5 if 7 ≤ x < 10, x/2 if 10 ≤ x ≤ 16}

d)

f^(-1)(x) = { x - 5 if 7 ≤ x < 10, x/2 if 10 ≤ x > 16}

36.

{ (𝑥, 𝑦) | 𝑥 divides 𝑦 } is it reflexive? antisymmetric? transitive?

a)

Maybe

b)

Sometimes

c)

Yes

d)

No

37.

{ (2,1), (2,3), (3,4), (4,3) }
Irreflexive?

symmetric?

a)

Irreflexive: No, Symmetric: Yes

b)

Irreflexive: Yes, Symmetric: No

c)

Irreflexive: Yes, Symmetric: Yes

d)

Irreflexive: No, Symmetric: No

38.

Determine if each function is one-to-one and/or onto. The possible
choices are:
𝑓: {5,7,9} → {3,4,5} , 𝑓(𝑛) = ⌈𝑛/2⌉

a)

Both

b)

One-to-one, onto

c)

Not one-to-one, not onto

d)

One-to-one, not onto

39.

Determine if each function is one-to-one and/or onto. The possible
choices are:

𝑓: ℤ → ℝ , 𝑓(𝑥) = 3𝑥 + 2

a)

Neither one-to-one nor onto

b)

One-to-one but not onto

c)

One-to-one and onto

d)

Onto but not one-to-one

40.

Let 𝑔: ℕ → ℚ , 𝑔(𝑥) = 2𝑥/𝑥+3 and ℎ: ℤ → ℕ , ℎ(𝑥) = 𝑥2 + 1 . Evaluate (𝑔 ∘ ℎ)(2).

a)

10/3

b)

1/4

c)

1/3

d)

5/4

41.

The function 𝑓(𝑥) ≡ 𝑥 (mod 5) , where the domain is {8, 9, 10, 11}, would be onto if the codomain
were...

a)

{0, 1, 3, 4}

b)

{1, 2, 3, 4}

c)

{0, 1, 2, 3, 5}

d)

{0, 1, 2, 3, 6}

42.

or the function 𝑓(𝑥) = √𝑥^2 − 9 , where the codomain is ℝ, which of the following is not a valid
way to define the domain?

a)

[5,8]

b)

[3,8]

c)

[2,5]

d)

??

MATH 170 A Quiz

Total questions: 42

Worksheet time: 23mins

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