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
, 12) x3 = 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 x3 = 8.
D) Three natural numbers x exist such that x3 = 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.
17) Write the negation of the following:
The test is difficult.
A) The test is not difficult. B) The test is not very easy.
C) The test is very difficult. D) The test is not easy.
Answer: A
18) Write the negation of the following:
8 + 2 = 10
A) 8 + 2 = 12 B) 8 + 2 = 2 + 8
C) The sum of 8 and 2 is ten. D) 8 + 2 ≠ 10
Answer: D
,SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide fan fappropriate fresponse.
19) Negate fthe ffollowing: fThe fstore fis fsometimes fopen fon
fSunday. fAnswer: f The fstore fis fnever fopen f on fSunday.
MULTIPLE fCHOICE. f Choose fthe fone falternative fthat fbest fcompletes fthe fstatement for fanswers fthe
fquestion. fConstruct fa ftruth ftable ffor fthe fstatement.
20) ~p f∧ f~s
A) p s (~p f ∧ f ~s) B) f p f f s f (~p f∧ f ~s) C) fp s (~p f∧ f ~s) D) f p f f s f (~p f∧ f ~s)
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: f C
21) s f∨ f~(r f∧ f p)
A) s r p s ∨ ~(r ∧ p) B) s r p s ∨ ~(r ∧ p)
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
A) p q t (p ∧ ~q) ∧ B) p q t (p ∧ ~q) ∧ 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
,23) ~((w ∧ q) ∨ s)
A) w q s ~((w ∧ q) ∨ s) B) w q s ~((w ∧ q) ∨ s)
T T T T T T T F
T T F F T T F F
T F T T T F T F
T F F F T F F T
F T T T F T T F
F T F F F T F T
F F T T F F T F
F F F F F F F T
Answer: B
24) w ∨ (w ∧ ~w)
A) w w ∨ (w ∧ ~w) B) w w ∨ (w ∧ ~w) C) w w ∨ (w ∧ ~w) D) w w ∨ (w ∧ ~w)
T T T F T T T F
F T F F F F F T
Answer: C
25) (t ∧ p) ∨ (~t ∧ ~p)
A) t p (t ∧ p) ∨ (~t ∧ ~p) B) t p (t ∧ p) ∨ (~t ∧ ~p)
T T F T T T
T F F T F F
F T T F T F
F F T F F T
C) t p (t p) ∨ (~t ∧ ~p)
∧ D) t p (t p) ∨ (~t ∧ ~p)
∧
T T T T F F
T F T F T F
F T T
F F F
Answer: f B
26) ~(~(s f∨ f p))
A) fs p ~(~(s f∨ fp)) B) f s p ~(~(s f∨ fp)) C) fs p ~(~(s f∨ fp)) D) fs p ~(~(s f ∨
f p))
T T T T T T T F T T T F
T F T T F T F T F T F F
F T T F T F F T F
F F F F F F F F T
Answer: A
, 27) ~(s f∨ ft) f ∧ f ~(t f ∧ f s)
A) fs t ~(s f∨ ft) f ∧ f ~(t B) f s t ~(s f∨ ft) f ∧ f ~(t
f ∧ f s) f ∧ f s)
T T F T T F
T F F T F F
F T F F T T
F F T F F F
C) fs t ~(s f∨ ft) f ∧ f ~(t D) fs t ~(s f∨ ft) f ∧ f ~(t
f ∧ f s) f ∧ f s)
T T F T T F
T F F T F T
F T F F T T
F F F F F F
Answer: f A
28) (p f∧ f w) f ∧ f (~w f∨ ft)
A) fp w t (p f∧ f w) f ∧ f (~w B) f p w t (p f∧ f w) f ∧
f∨ f t) f (~w f ∨ ft)
T T T F T T T T
T T F T T T F F
T F T T T F T F
T F F T T F F F
F T T T F T T F
F T F F F T F F
F F T T F F T F
F F F T F F F F
Answer: B
Letting fr fstand ffor f"The ffood fis fgood," fp fstand ffor f"I feat ftoo fmuch," fand fq fstand ffor f"I'll fexercise," fwrite fthe
ffollowing fin fsymbolic fform.
29) If fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f→ fp B) fp f∨ fq C) fq f→ fp D) fp f→
fq fAnswer: f D
30) If fI fexercise, fthen fI fwon't feat ftoo fmuch.
A) p f→ fq B) fq f→ f~p C) fr f∧ fp D) f~(p f→
fq) fAnswer: f B
31) If fthe ffood fis fgood, fthen fI feat ftoo fmuch.
A) r f→ fp B) fr f∧ fp C) fp f→ fq D) fp f→
fr fAnswer: f A
32) If fthe ffood fis fgood fand fif fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f→ f(p f∧ fq) B) f(r f∧ fp) f→ fq C) fr f∧ f(p f→ fq) D) fp f→ f(r f∧
fq) fAnswer: f B
33) If fthe ffood fis fgood for fif fI feat ftoo fmuch, fI'll fexercise.
A) r f→ f(p f∨ fq) B) f(r f∧ fp) f→ fq C) fr f→ fp f→ fq D) f(r f∨ fp)
f→ fq fAnswer: f D
, 34) If fthe ffood fis fnot fgood, fI fwon't feat ftoo fmuch.
A) f~r f→ f~p B) fr f→ f~p C) f~(r f→ fp) D) f~p f→
f~r fAnswer: fA
35) I'll fexercise fif fI feat ftoo fmuch.
A) p f∨ fq B) fq f→ fp C) fp f→ fq D) fq f∧
fp fAnswer: f C
36) The ffood fis fgood fand fif fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f∧ f(p f→ fq) B) f(r f∨ fp) f→ f q C) f(r f→ fp) f∨ fq D) f(r f∧ fp)
f→ fq fAnswer: f A
37) I'll fexercise fif fI fdon't feat ftoo fmuch.
A) f~(p f→ fq) B) f~p f∧ fq C) f~p f→ fq D) f~p f∨
fq fAnswer: f C
38) If fI fexercise, fthen fthe ffood fwon't fbe fgood fand fI fwon't feat ftoo fmuch.
A) f(q f∧ f~r) f→ f~p B) fq f→ f~(r f∧ fp) C) f~(r f∧ fp) f→ fq D) fq f→ f(~r f∧
f~p) fAnswer: f D
Restate fin fa flogically fequivalent fform.
39) It fis fnot ftrue fthat fboth fthis fbook fis finteresting fand fthe fbook fis fabout fstars.
A) Either fthis fbook fis fnot finteresting for fit fis fnot fabout fstars.
B) This fbook fis fboth finteresting fand fabout fstars.
C) Either fthis fbook fis finteresting for fit fis fabout fstars.
D) This fbook fcannot fbe fboth finteresting fand fabout
fstars. fAnswer: f A
40) If fa fnumber fis fdivisible fby f4, fthen fit fis fdivisible fby f2.
A) If fa fnumber fis fnot fdivisible fby f4, fthen fit fis fdivisible fby f2.
B) If fa fnumber fis fnot fdivisible fby f4, fthen fit fis fnot fdivisible fby f2.
C) If fa fnumber fis fdivisible fby f4, fthen fit fis fnot fdivisible fby f2.
D) If fa fnumber fis fnot fdivisible fby f2, fthen fit fis fnot
fdivisible fby f4. fAnswer: f D
41) If fit fis fclean, fthen fit fwas fwashed.
A) If fit fwas fnot fwashed, fthen fit fis fnot fclean. B) f If fit fis fclean, fthen fit fwas fnot fwashed.
C) fIf fit fis fclean, fthen fit fwas fwashed. D) fIf fit fis fnot fclean, fthen fit fwas fnot
fwashed. fAnswer: f A
42) It fis fnot ftrue fthat ftoday fI fboth fwent fto fschool fand fread fa fbook.
A) Today, fI fread fa fbook fbut fdid fnot fgo fto fschool.
B) Today, fI feither fdid fnot fgo fto fschool for fI fdid fnot fread fa fbook.
C) Today, fI fwent fto fschool fand fread fa fbook.
D) Today, fI fdid fnot fread fa fbook fand fdid fnot fgo
fto fschool. fAnswer: f B
,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
, 12) x3 = 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 x3 = 8.
D) Three natural numbers x exist such that x3 = 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.
17) Write the negation of the following:
The test is difficult.
A) The test is not difficult. B) The test is not very easy.
C) The test is very difficult. D) The test is not easy.
Answer: A
18) Write the negation of the following:
8 + 2 = 10
A) 8 + 2 = 12 B) 8 + 2 = 2 + 8
C) The sum of 8 and 2 is ten. D) 8 + 2 ≠ 10
Answer: D
,SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide fan fappropriate fresponse.
19) Negate fthe ffollowing: fThe fstore fis fsometimes fopen fon
fSunday. fAnswer: f The fstore fis fnever fopen f on fSunday.
MULTIPLE fCHOICE. f Choose fthe fone falternative fthat fbest fcompletes fthe fstatement for fanswers fthe
fquestion. fConstruct fa ftruth ftable ffor fthe fstatement.
20) ~p f∧ f~s
A) p s (~p f ∧ f ~s) B) f p f f s f (~p f∧ f ~s) C) fp s (~p f∧ f ~s) D) f p f f s f (~p f∧ f ~s)
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: f C
21) s f∨ f~(r f∧ f p)
A) s r p s ∨ ~(r ∧ p) B) s r p s ∨ ~(r ∧ p)
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
A) p q t (p ∧ ~q) ∧ B) p q t (p ∧ ~q) ∧ 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
,23) ~((w ∧ q) ∨ s)
A) w q s ~((w ∧ q) ∨ s) B) w q s ~((w ∧ q) ∨ s)
T T T T T T T F
T T F F T T F F
T F T T T F T F
T F F F T F F T
F T T T F T T F
F T F F F T F T
F F T T F F T F
F F F F F F F T
Answer: B
24) w ∨ (w ∧ ~w)
A) w w ∨ (w ∧ ~w) B) w w ∨ (w ∧ ~w) C) w w ∨ (w ∧ ~w) D) w w ∨ (w ∧ ~w)
T T T F T T T F
F T F F F F F T
Answer: C
25) (t ∧ p) ∨ (~t ∧ ~p)
A) t p (t ∧ p) ∨ (~t ∧ ~p) B) t p (t ∧ p) ∨ (~t ∧ ~p)
T T F T T T
T F F T F F
F T T F T F
F F T F F T
C) t p (t p) ∨ (~t ∧ ~p)
∧ D) t p (t p) ∨ (~t ∧ ~p)
∧
T T T T F F
T F T F T F
F T T
F F F
Answer: f B
26) ~(~(s f∨ f p))
A) fs p ~(~(s f∨ fp)) B) f s p ~(~(s f∨ fp)) C) fs p ~(~(s f∨ fp)) D) fs p ~(~(s f ∨
f p))
T T T T T T T F T T T F
T F T T F T F T F T F F
F T T F T F F T F
F F F F F F F F T
Answer: A
, 27) ~(s f∨ ft) f ∧ f ~(t f ∧ f s)
A) fs t ~(s f∨ ft) f ∧ f ~(t B) f s t ~(s f∨ ft) f ∧ f ~(t
f ∧ f s) f ∧ f s)
T T F T T F
T F F T F F
F T F F T T
F F T F F F
C) fs t ~(s f∨ ft) f ∧ f ~(t D) fs t ~(s f∨ ft) f ∧ f ~(t
f ∧ f s) f ∧ f s)
T T F T T F
T F F T F T
F T F F T T
F F F F F F
Answer: f A
28) (p f∧ f w) f ∧ f (~w f∨ ft)
A) fp w t (p f∧ f w) f ∧ f (~w B) f p w t (p f∧ f w) f ∧
f∨ f t) f (~w f ∨ ft)
T T T F T T T T
T T F T T T F F
T F T T T F T F
T F F T T F F F
F T T T F T T F
F T F F F T F F
F F T T F F T F
F F F T F F F F
Answer: B
Letting fr fstand ffor f"The ffood fis fgood," fp fstand ffor f"I feat ftoo fmuch," fand fq fstand ffor f"I'll fexercise," fwrite fthe
ffollowing fin fsymbolic fform.
29) If fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f→ fp B) fp f∨ fq C) fq f→ fp D) fp f→
fq fAnswer: f D
30) If fI fexercise, fthen fI fwon't feat ftoo fmuch.
A) p f→ fq B) fq f→ f~p C) fr f∧ fp D) f~(p f→
fq) fAnswer: f B
31) If fthe ffood fis fgood, fthen fI feat ftoo fmuch.
A) r f→ fp B) fr f∧ fp C) fp f→ fq D) fp f→
fr fAnswer: f A
32) If fthe ffood fis fgood fand fif fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f→ f(p f∧ fq) B) f(r f∧ fp) f→ fq C) fr f∧ f(p f→ fq) D) fp f→ f(r f∧
fq) fAnswer: f B
33) If fthe ffood fis fgood for fif fI feat ftoo fmuch, fI'll fexercise.
A) r f→ f(p f∨ fq) B) f(r f∧ fp) f→ fq C) fr f→ fp f→ fq D) f(r f∨ fp)
f→ fq fAnswer: f D
, 34) If fthe ffood fis fnot fgood, fI fwon't feat ftoo fmuch.
A) f~r f→ f~p B) fr f→ f~p C) f~(r f→ fp) D) f~p f→
f~r fAnswer: fA
35) I'll fexercise fif fI feat ftoo fmuch.
A) p f∨ fq B) fq f→ fp C) fp f→ fq D) fq f∧
fp fAnswer: f C
36) The ffood fis fgood fand fif fI feat ftoo fmuch, fthen fI'll fexercise.
A) r f∧ f(p f→ fq) B) f(r f∨ fp) f→ f q C) f(r f→ fp) f∨ fq D) f(r f∧ fp)
f→ fq fAnswer: f A
37) I'll fexercise fif fI fdon't feat ftoo fmuch.
A) f~(p f→ fq) B) f~p f∧ fq C) f~p f→ fq D) f~p f∨
fq fAnswer: f C
38) If fI fexercise, fthen fthe ffood fwon't fbe fgood fand fI fwon't feat ftoo fmuch.
A) f(q f∧ f~r) f→ f~p B) fq f→ f~(r f∧ fp) C) f~(r f∧ fp) f→ fq D) fq f→ f(~r f∧
f~p) fAnswer: f D
Restate fin fa flogically fequivalent fform.
39) It fis fnot ftrue fthat fboth fthis fbook fis finteresting fand fthe fbook fis fabout fstars.
A) Either fthis fbook fis fnot finteresting for fit fis fnot fabout fstars.
B) This fbook fis fboth finteresting fand fabout fstars.
C) Either fthis fbook fis finteresting for fit fis fabout fstars.
D) This fbook fcannot fbe fboth finteresting fand fabout
fstars. fAnswer: f A
40) If fa fnumber fis fdivisible fby f4, fthen fit fis fdivisible fby f2.
A) If fa fnumber fis fnot fdivisible fby f4, fthen fit fis fdivisible fby f2.
B) If fa fnumber fis fnot fdivisible fby f4, fthen fit fis fnot fdivisible fby f2.
C) If fa fnumber fis fdivisible fby f4, fthen fit fis fnot fdivisible fby f2.
D) If fa fnumber fis fnot fdivisible fby f2, fthen fit fis fnot
fdivisible fby f4. fAnswer: f D
41) If fit fis fclean, fthen fit fwas fwashed.
A) If fit fwas fnot fwashed, fthen fit fis fnot fclean. B) f If fit fis fclean, fthen fit fwas fnot fwashed.
C) fIf fit fis fclean, fthen fit fwas fwashed. D) fIf fit fis fnot fclean, fthen fit fwas fnot
fwashed. fAnswer: f A
42) It fis fnot ftrue fthat ftoday fI fboth fwent fto fschool fand fread fa fbook.
A) Today, fI fread fa fbook fbut fdid fnot fgo fto fschool.
B) Today, fI feither fdid fnot fgo fto fschool for fI fdid fnot fread fa fbook.
C) Today, fI fwent fto fschool fand fread fa fbook.
D) Today, fI fdid fnot fread fa fbook fand fdid fnot fgo
fto fschool. fAnswer: f B
