x
,MULTIPLE xCHOICE. x Choose xthe xone xalternative x that xbest xcompletes xthe xstatement xor xanswers xthe xquestion.
Determine x whether xthe xfollowing xis xa xstatement. xIf xit xis, xthen xalso xclassify xthe xstatement xas xtrue xor xfalse.
1) Why xdon't xyou xcome xhere?
A) Not xa xstatement B) xFalse xstatement C) xTrue
xstatement xAnswer: x A
2) This xroom xis xbig.
A) True xstatement B) xNot xa xstatement C) xFalse
xstatement xAnswer: x B
3) 5 x- x1 x= x4
A) True xstatement B) xNot xa xstatement C) xFalse
xstatement xAnswer: x A
4) 7x x + xy x= x3
A) False xstatement B) xTrue xstatement C) xNot xa
xstatement xAnswer: x C
5) Can xyou xbring xthe xbook?
A) True xstatement B) xNot xa xstatement C) xFalse
xstatement xAnswer: x B
6) x x+ xy x= xx x- xy, xwhere x y x= x0
A) False xstatement B) xTrue xstatement C) xNot xa
xstatement xAnswer: x B
7) 12 x = x3y
A) Not xa xstatement B) xFalse xstatement C) xTrue
xstatement xAnswer: x A
8) 2.4 x = x5.2
A) False xstatement B) xNot xa xstatement C) xTrue
xstatement xAnswer: x A
9) The xstate xof xCalifornia xis xin xNorth xAmerica.
A) Not xa xstatement B) xFalse xstatement C) xTrue
xstatement xAnswer: x C
10) Brazil xis xin xAsia.
A) True xstatement B) xNot xa xstatement C) xFalse
xstatement xAnswer: x C
Use xa xquantifier x to xmake x the xfollowing xtrue x or xfalse, xas xindicated, xwhere xx xis xa xnatural xnumber.
11) x x+ xx x= x6 x (make xtrue)
A) There xis xno xnatural xnumber xx xsuch xthat xx x+ xx x= x6.
B) For xall xnatural xnumbers xx, xx x+ xx x= x6.
C) There xexists xa xnatural xnumber xx xsuch xthat xx x+ xx x= x6.
D) For xevery xnatural xnumber xx, xx x+ xx x= x6.
Answer:
xC
, 12) x3 x = x8 x x (make xtrue)
A) No xnatural xnumber xx xexists xsuch xthat xx3 x= x8.
B) Every xnatural xnumber xx xsatisfies xx3 x= x8.
C) There xexists x a xnatural xnumber xx xsuch xthat xx3 x= x8.
D) Three xnatural xnumbers xx xexist xsuch xthat xx3
= x8. xAnswer:
x
x C
13) 2x x+ x1 x= x5 x- xx x (make xtrue)
A) No xnatural xnumber xx xexists xsuch xthat x2x x+ x1 x = x5 x - xx.
B) There xexists xa xnatural x number xx xsuch xthat x2x x+ x1 x = x5 x- xx.
C) Only xtwo xnatural xnumbers xx xexist xsuch x that x2x x + x1 x= x5 x- xx.
D) For xevery xnatural xnumber xx, x2x x+ x1 x=
x5 x- xx. xAnswer: x B
14) 12x x= x5x x + x7x x (make xfalse)
A) For xevery xnatural xnumber xx, x12x x= x5x x+ x7x.
B) There xis xno xnatural xnumber xx xsuch xthat x12x x= x5x x+ x7x.
C) More xthan xone xnatural xnumber xx xexists xsuch xthat x12x x= x5x x+ x7x.
D) There xexists xa xnatural xnumber xx xsuch xthat x12x x= x5x
x+ x7x. xAnswer: x B
15) x x- x13 x= x13 x- xx x (make xfalse)
A) For xx x= x13, xx x- x13 x= x13 x- x x.
B) There xexists xa x natural x number xx xsuch xthat xx x- x13 x= x13 x- xx.
C) At xleast xone xnatural xnumber xx xexists xsuch xthat xx x - x13 x= x13 x- xx.
D) There xis xno xnatural xnumber xx xsuch xthat xx x- x13 x=
x13 x- xx. xAnswer: xD
16) 4x x = x7x x x (make xfalse)
A) There xis xno xnatural xnumber xx xsuch xthat x4x x= x7x.
B) For xevery xnatural x number xx, x4x x= x7x.
C) No xnatural xnumber xx xsatisfies x4x x=
x7x. xAnswer: x B
Write xthe x statement x indicated.
17) Write xthe xnegation xof xthe
xfollowing: xThe xtest xis xdifficult.
A) The xtest xis xnot xdifficult. B) xThe xtest xis xnot xvery xeasy.
C) xThe xtest xis xvery xdifficult. D) xThe xtest xis xnot
easy. xAnswer:
x x A
18) Write xthe xnegation xof xthe
xfollowing: x8 x+ x2 x= x10
A) 8 x+ x2 x= x12 B) x 8 x+ x2 x= x2 x+ x8
C) xThe xsum xof x8 xand x2 xis xten. D) x8 x+ x2 x≠ x10
Answer:
xD
, SHORT xANSWER. x Write x the xword xor xphrase x that xbest xcompletes xeach xstatement xor x answers xthe x question.
Provide xan xappropriate x response.
19) Negate xthe xfollowing: xThe xstore xis xsometimes xopen xon
Sunday. xAnswer:
x x The xstore xis xnever xopen xon xSunday.
MULTIPLE xCHOICE. x Choose xthe xone xalternative xthat xbest xcompletes xthe xstatement xor xanswers xthe
x question. xConstruct xa xtruth xtable xfor xthe xstatement.
20) ~p x∧ x~s
A) p s (~p x ∧ x ~s) B) x p x x s x (~p x∧ x ~s) C) xp s (~p x∧ x ~s) D) xp x x s x (~p x∧ x ~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: x C
21) s x∨ x~(r x∧ x p)
A) xs r p s x∨ x~(r x∧ B) x s r p s x∨ x~(r x∧
x p) x 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 x∧ x ~q) x ∧ x t
A) xp q t (p x∧ x ~q) B) x p q t (p x∧ x ~q) x∧
x∧ x 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: x B