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