TEST BANK
,MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the following is a statement. If it is, then also classify the statement as true or false.
1) Why don't you come here?
A) Not a statement B) False statement C) True statement
Answer: A
2) This room is big.
A) True statement B) Not a statement C) False statement
Answer: B
3) 5 - 1 = 4
A) True statement B) Not a statement C) False statement
Answer: A
4) 7x + y = 3
A) False statement B) True statement C) Not a statement
Answer: C
5) Can you bring the book?
A) True statement B) Not a statement C) False statement
Answer: B
6) x + y = x - y, where y = 0
A) False statement B) True statement C) Not a statement
Answer: B
7) 12 = 3y
A) Not a statement B) False statement C) True statement
Answer: A
8) 2.4 = 5.2
A) False statement B) Not a statement C) True statement
Answer: A
9) The state of California is in North America.
A) Not a statement B) False statement C) True statement
Answer: C
10) Brazil is in Asia.
A) True statement B) Not a statement C) False statement
Answer: C
Use a quantifier to make the following true or false, as indicated, where x is a natural number.
11) x + x = 6 (make true)
A) There is no natural number x such that x + x = 6.
B) For all natural numbers x, x + x = 6.
C) There exists a natural number x such that x + x = 6.
D) For every natural number x, x + x = 6.
Answer: C
, 3
12) x = 8 (make true)
A) No natural number x exists such that x3 = 8.
B) Every natural number x satisfies x3 = 8.
C) There exists a natural number x such that x = 8.
3
D) Three natural numbers x exist such that x
3 = 8.
Answer: C
13) 2x + 1 = 5 - x (make true)
A) No natural number x exists such that 2x + 1 = 5 - x.
B) There exists a natural number x such that 2x + 1 = 5 - x.
C) Only two natural numbers x exist such that 2x + 1 = 5 - x.
D) For every natural number x, 2x + 1 = 5 - x.
Answer: B
14) 12x = 5x + 7x (make false)
A) For every natural number x, 12x = 5x + 7x.
B) There is no natural number x such that 12x = 5x + 7x.
C) More than one natural number x exists such that 12x = 5x + 7x.
D) There exists a natural number x such that 12x = 5x + 7x.
Answer: B
15) x - 13 = 13 - x (make false)
A) For x = 13, x - 13 = 13 - x.
B) There exists a natural number x such that x - 13 = 13 - x.
C) At least one natural number x exists such that x - 13 = 13 - x.
D) There is no natural number x such that x - 13 = 13 - x.
Answer: D
16) 4x = 7x (make false)
A) There is no natural number x such that 4x = 7x.
B) For every natural number x, 4x = 7x.
C) No natural number x satisfies 4x = 7x.
Answer: B
Write the statement indicated.
z z z
17) Write the negation of the following: z z z z z z
The test is difficult. z z z z
A) The test is not difficult.
z z z z z B) The test is not very easy.
z z z z z z
C) The test is very difficult.
z z z z z D) The test is not easy.
z z z z z
Answer: A z
18) Write the negation of the following: 8 z z z z z z z
+ 2 = 10 z z z z
A) 8 + 2 = 12 z z z z z B) 8 + 2 = 2 + 8
z z z z z z z
C) The sum of 8 and 2 is ten. z z z z z z z z D) 8 + 2 ≠10
z z z z
Answer: D z
, SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
z z z z z z z z z z z z z z z
Provide an appropriate response.
z z z
19) Negate the following: The store is sometimes open on Sunday. z z z z z z z z z z
Answer: The store is never open on Sunday. z z z z z z z z
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
z z z z z z z z z z z z z z
Construct a truth table for the statement.
z z z z z z
20) ~p ∧ ~s z z z
A) p s (~p ∧ ~s) z z z z z z B) p s (~p ∧ ~s)
z z z z z z C) p sz z z z (~p ∧ ~s)
z z D) p s (~p ∧ ~s)
z z z z z z
T T T T T F T T F T T F
T F F T F F T F F T F T
F T F F T F F T F F T T
F F T F F F F F T F F T
Answer: C z
21) s ∨ ~(r ∧ p)
z z z z z
A) s z r p s ∨ ~(r ∧ p)z z z z B) s z r p s ∨ ~(r ∧ p)
z z z z
T T T T T T T T
T T F T T T F T
T F T T T F T T
T F F T T F F T
F T T F F T T F
F T F T F T F T
F F T T F F T T
F F F F F F F T
Answer: B z z
22) (p ∧ ~q) ∧ t z z z z z
A) p q t z (p ∧ ~q) ∧ z z z B) p z q t (p ∧ ~q) ∧ tz z z z
T T T F T T T F
T T F F T T F F
T F T F T F T T
T F F F T F F F
F T T F F T T F
F T F T F T F F
F F T T F F T F
F F F T F F F F
Answer: B z
,MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the following is a statement. If it is, then also classify the statement as true or false.
1) Why don't you come here?
A) Not a statement B) False statement C) True statement
Answer: A
2) This room is big.
A) True statement B) Not a statement C) False statement
Answer: B
3) 5 - 1 = 4
A) True statement B) Not a statement C) False statement
Answer: A
4) 7x + y = 3
A) False statement B) True statement C) Not a statement
Answer: C
5) Can you bring the book?
A) True statement B) Not a statement C) False statement
Answer: B
6) x + y = x - y, where y = 0
A) False statement B) True statement C) Not a statement
Answer: B
7) 12 = 3y
A) Not a statement B) False statement C) True statement
Answer: A
8) 2.4 = 5.2
A) False statement B) Not a statement C) True statement
Answer: A
9) The state of California is in North America.
A) Not a statement B) False statement C) True statement
Answer: C
10) Brazil is in Asia.
A) True statement B) Not a statement C) False statement
Answer: C
Use a quantifier to make the following true or false, as indicated, where x is a natural number.
11) x + x = 6 (make true)
A) There is no natural number x such that x + x = 6.
B) For all natural numbers x, x + x = 6.
C) There exists a natural number x such that x + x = 6.
D) For every natural number x, x + x = 6.
Answer: C
, 3
12) x = 8 (make true)
A) No natural number x exists such that x3 = 8.
B) Every natural number x satisfies x3 = 8.
C) There exists a natural number x such that x = 8.
3
D) Three natural numbers x exist such that x
3 = 8.
Answer: C
13) 2x + 1 = 5 - x (make true)
A) No natural number x exists such that 2x + 1 = 5 - x.
B) There exists a natural number x such that 2x + 1 = 5 - x.
C) Only two natural numbers x exist such that 2x + 1 = 5 - x.
D) For every natural number x, 2x + 1 = 5 - x.
Answer: B
14) 12x = 5x + 7x (make false)
A) For every natural number x, 12x = 5x + 7x.
B) There is no natural number x such that 12x = 5x + 7x.
C) More than one natural number x exists such that 12x = 5x + 7x.
D) There exists a natural number x such that 12x = 5x + 7x.
Answer: B
15) x - 13 = 13 - x (make false)
A) For x = 13, x - 13 = 13 - x.
B) There exists a natural number x such that x - 13 = 13 - x.
C) At least one natural number x exists such that x - 13 = 13 - x.
D) There is no natural number x such that x - 13 = 13 - x.
Answer: D
16) 4x = 7x (make false)
A) There is no natural number x such that 4x = 7x.
B) For every natural number x, 4x = 7x.
C) No natural number x satisfies 4x = 7x.
Answer: B
Write the statement indicated.
z z z
17) Write the negation of the following: z z z z z z
The test is difficult. z z z z
A) The test is not difficult.
z z z z z B) The test is not very easy.
z z z z z z
C) The test is very difficult.
z z z z z D) The test is not easy.
z z z z z
Answer: A z
18) Write the negation of the following: 8 z z z z z z z
+ 2 = 10 z z z z
A) 8 + 2 = 12 z z z z z B) 8 + 2 = 2 + 8
z z z z z z z
C) The sum of 8 and 2 is ten. z z z z z z z z D) 8 + 2 ≠10
z z z z
Answer: D z
, SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
z z z z z z z z z z z z z z z
Provide an appropriate response.
z z z
19) Negate the following: The store is sometimes open on Sunday. z z z z z z z z z z
Answer: The store is never open on Sunday. z z z z z z z z
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
z z z z z z z z z z z z z z
Construct a truth table for the statement.
z z z z z z
20) ~p ∧ ~s z z z
A) p s (~p ∧ ~s) z z z z z z B) p s (~p ∧ ~s)
z z z z z z C) p sz z z z (~p ∧ ~s)
z z D) p s (~p ∧ ~s)
z z z z z z
T T T T T F T T F T T F
T F F T F F T F F T F T
F T F F T F F T F F T T
F F T F F F F F T F F T
Answer: C z
21) s ∨ ~(r ∧ p)
z z z z z
A) s z r p s ∨ ~(r ∧ p)z z z z B) s z r p s ∨ ~(r ∧ p)
z z z z
T T T T T T T T
T T F T T T F T
T F T T T F T T
T F F T T F F T
F T T F F T T F
F T F T F T F T
F F T T F F T T
F F F F F F F T
Answer: B z z
22) (p ∧ ~q) ∧ t z z z z z
A) p q t z (p ∧ ~q) ∧ z z z B) p z q t (p ∧ ~q) ∧ tz z z z
T T T F T T T F
T T F F T T F F
T F T F T F T T
T F F F T F F F
F T T F F T T F
F T F T F T F F
F F T T F F T F
F F F T F F F F
Answer: B z
