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,MULTIPLE x CHOICE. x Choose x the x one x alternative x that x best x completes x the x statement x or x answers x the x question.
Determine x whether x the x following x is x a x statement. x If x it x is, x then x also x classify x the x statement x as x true x or x false.
1) Why xdon't xyou xcome xhere?
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x A
2) This xroom x is xbig.
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x B
3) 5 x- x1 x= x4
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x A
4) 7x x+ xy x= x3
A) False xstatement B) xTrue xstatement C) xNot xa xstatement
x Answer: x C
5) Can xyou xbring xthe xbook?
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x B
6) x x+ xy x= xx x- xy, xwhere xy x= x0
A) False xstatement B) xTrue xstatement C) xNot xa xstatement
x Answer: x B
7) 12 x= x3y
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x A
8) 2.4 x = x5.2
A) False xstatement B) xNot xa xstatement C) xTrue xstatement
x Answer: x A
9) The xstate xof xCalifornia x is xin x North xAmerica.
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x C
10) Brazil x is xin xAsia.
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x C
Use x a x quantifier x to xmake x the x following xtrue x or x false, xas x indicated, x where x x x is x a x natural x number.
11) x x+ x x x= x6 x (make xtrue)
A) There x is xno xnatural x number xx x such xthat xx x+ xx x= x6.
B) For xall x natural x numbers xx, xx x+ x x 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. xAnswer: x C
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, 12) x3 x= x8 x (make xtrue)
A) No xnatural xnumber xx xexists xsuch xthat xx3 x= x8.
B) Every x natural x number x x x satisfies x x3 x = x8.
C) There xexists xa xnatural xnumber xx xsuch xthat xx3 x= x8.
D) Three xnatural xnumbers xx xexist xsuch xthat xx3 x= x8.
x Answer: x C
13) 2x x+ x1 x= x5 x- xx x (make xtrue)
A) No xnatural x number xx x exists x such x that x2x x+ x1 x = x5 x - x x.
B) There x exists x a x natural x number xx x such xthat x2x x+ x1 x = x5 x - x x.
C) Only xtwo xnatural xnumbers xx xexist xsuch xthat x2x x+ x1 x= x5 x- xx.
D) For xevery xnatural xnumber xx, x2x x+ x1 x= x5 x- xx.
x Answer: x B
14) 12x x= x5x x+ x7x x (make xfalse)
A) For xevery x natural x number xx, x12x x = x5x x + x7x.
B) There x is xno xnatural x number xx x such xthat x12x x = x5x x + x7x.
C) More xthan x one xnatural x number xx x exists x such xthat x 12x x = x5x x + x7x.
D) There xexists xa xnatural xnumber xx xsuch xthat x12x x= x5x x+
x 7x. 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- xx.
B) There x exists x a x natural x number x x x such x that x x x - x 13 x= x13 x - x x.
C) At x least x one x natural x number x x x exists x such x that x x x - x13 x= x13 x- x x.
D) There xis xno xnatural xnumber xx xsuch xthat xx x- x13 x= x13 x-
x x. xAnswer: xD
16) 4x x= x7x x (make xfalse)
A) There xis xno xnatural xnumber xx xsuch xthat x4x x= x7x.
B) For x every x natural x number x x, x4x x = x7x.
C) No xnatural xnumber xx xsatisfies x4x x= x7x.
x Answer: x B
Write x the x statement x indicated.
17) Write xthe xnegation xof xthe xfollowing:
xThe xtest xis xdifficult.
A) The xtest xis xnot xdifficult. B) x The xtest xis xnot xvery xeasy.
C) xThe xtest xis xvery xdifficult. D) xThe xtest xis xnot
x easy. xAnswer: x A
18) Write xthe xnegation xof xthe xfollowing:
x8 x+ x2 x= x10
A) 8 x + x 2 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≠
10 xAnswer: x D
x
3
, SHORT x ANSWER. x Write x the x word x or x phrase x that x best x completes x each x statement x or x answers x the x question.
Provide x an x appropriate x response.
19) Negate xthe xfollowing: xThe xstore xis xsometimes xopen xon
Sunday. xAnswer: x The xstore xis xnever xopen xon xSunday.
x
MULTIPLE x CHOICE. x Choose x the x one x alternative x that x best x completes x the x statement x or x answers x the x question.
Construct xa x truth x table x for x the
x statement.
20) ~p x∧ x~s B) p x x s x (~p x∧ C) p s (~p x∧ x ~s) D) p x x s x (~p x∧ x ~s)
A) p s (~p x∧ x ~s) 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) x s 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∧ xt
A) x p q t (p x∧ x ~q) x∧ xt B) x p q t (p x∧ x ~q) 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
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,MULTIPLE x CHOICE. x Choose x the x one x alternative x that x best x completes x the x statement x or x answers x the x question.
Determine x whether x the x following x is x a x statement. x If x it x is, x then x also x classify x the x statement x as x true x or x false.
1) Why xdon't xyou xcome xhere?
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x A
2) This xroom x is xbig.
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x B
3) 5 x- x1 x= x4
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x A
4) 7x x+ xy x= x3
A) False xstatement B) xTrue xstatement C) xNot xa xstatement
x Answer: x C
5) Can xyou xbring xthe xbook?
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x B
6) x x+ xy x= xx x- xy, xwhere xy x= x0
A) False xstatement B) xTrue xstatement C) xNot xa xstatement
x Answer: x B
7) 12 x= x3y
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x A
8) 2.4 x = x5.2
A) False xstatement B) xNot xa xstatement C) xTrue xstatement
x Answer: x A
9) The xstate xof xCalifornia x is xin x North xAmerica.
A) Not xa xstatement B) xFalse xstatement C) xTrue xstatement
x Answer: x C
10) Brazil x is xin xAsia.
A) True xstatement B) xNot xa xstatement C) xFalse xstatement
x Answer: x C
Use x a x quantifier x to xmake x the x following xtrue x or x false, xas x indicated, x where x x x is x a x natural x number.
11) x x+ x x x= x6 x (make xtrue)
A) There x is xno xnatural x number xx x such xthat xx x+ xx x= x6.
B) For xall x natural x numbers xx, xx x+ x x 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. xAnswer: x C
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, 12) x3 x= x8 x (make xtrue)
A) No xnatural xnumber xx xexists xsuch xthat xx3 x= x8.
B) Every x natural x number x x x satisfies x x3 x = x8.
C) There xexists xa xnatural xnumber xx xsuch xthat xx3 x= x8.
D) Three xnatural xnumbers xx xexist xsuch xthat xx3 x= x8.
x Answer: x C
13) 2x x+ x1 x= x5 x- xx x (make xtrue)
A) No xnatural x number xx x exists x such x that x2x x+ x1 x = x5 x - x x.
B) There x exists x a x natural x number xx x such xthat x2x x+ x1 x = x5 x - x x.
C) Only xtwo xnatural xnumbers xx xexist xsuch xthat x2x x+ x1 x= x5 x- xx.
D) For xevery xnatural xnumber xx, x2x x+ x1 x= x5 x- xx.
x Answer: x B
14) 12x x= x5x x+ x7x x (make xfalse)
A) For xevery x natural x number xx, x12x x = x5x x + x7x.
B) There x is xno xnatural x number xx x such xthat x12x x = x5x x + x7x.
C) More xthan x one xnatural x number xx x exists x such xthat x 12x x = x5x x + x7x.
D) There xexists xa xnatural xnumber xx xsuch xthat x12x x= x5x x+
x 7x. 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- xx.
B) There x exists x a x natural x number x x x such x that x x x - x 13 x= x13 x - x x.
C) At x least x one x natural x number x x x exists x such x that x x x - x13 x= x13 x- x x.
D) There xis xno xnatural xnumber xx xsuch xthat xx x- x13 x= x13 x-
x x. xAnswer: xD
16) 4x x= x7x x (make xfalse)
A) There xis xno xnatural xnumber xx xsuch xthat x4x x= x7x.
B) For x every x natural x number x x, x4x x = x7x.
C) No xnatural xnumber xx xsatisfies x4x x= x7x.
x Answer: x B
Write x the x statement x indicated.
17) Write xthe xnegation xof xthe xfollowing:
xThe xtest xis xdifficult.
A) The xtest xis xnot xdifficult. B) x The xtest xis xnot xvery xeasy.
C) xThe xtest xis xvery xdifficult. D) xThe xtest xis xnot
x easy. xAnswer: x A
18) Write xthe xnegation xof xthe xfollowing:
x8 x+ x2 x= x10
A) 8 x + x 2 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≠
10 xAnswer: x D
x
3
, SHORT x ANSWER. x Write x the x word x or x phrase x that x best x completes x each x statement x or x answers x the x question.
Provide x an x appropriate x response.
19) Negate xthe xfollowing: xThe xstore xis xsometimes xopen xon
Sunday. xAnswer: x The xstore xis xnever xopen xon xSunday.
x
MULTIPLE x CHOICE. x Choose x the x one x alternative x that x best x completes x the x statement x or x answers x the x question.
Construct xa x truth x table x for x the
x statement.
20) ~p x∧ x~s B) p x x s x (~p x∧ C) p s (~p x∧ x ~s) D) p x x s x (~p x∧ x ~s)
A) p s (~p x∧ x ~s) 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) x s 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∧ xt
A) x p q t (p x∧ x ~q) x∧ xt B) x p q t (p x∧ x ~q) 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
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