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