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Questions in this quiz (40)
1Which of the following sentences is a proposition?
- ACan you help me?
- BTake this pencil.
- Cx + 2 = 6
- D3 + 2 = 6
2Let p be a proposition. The statement “It is not the case that p” is denoted by
- A⊕ p
- Bp →¬p
- C¬p
- Dp ∧ ¬p
3Let p and q be propositions. The proposition that is true when both p and q are true and is false otherwise is denoted by
- Ap ∨ q
- Bp → q
- Cp ↔ q
- Dp ∧ q
4Let p and q be propositions. The proposition that is false when p and q are both false
and is true otherwise is denoted by- Ap → q
- Bp ∨ q
- Cp ∧ q
- Dp ↔ q
5Let p and q be propositions. The proposition that is true when exactly one of p and q is true and is false otherwise is denoted by
- Ap ∨ q
- Bp → q
- Cp ⊕ q
- Dp ↔ q
6Let p and q be propositions. The proposition that is false when p is true and q is false and is true otherwise is denoted by
- Ap → q
- Bp ∨ q
- Cp ∧ q
- Dp ↔ q
7Let p and q be propositions. The proposition that is true when p and q have the same truth values and is false otherwise is denoted by
- Ap ∨ q
- Bp → q
- Cp ↔ q
- Dp ∧ q
8Find the converse of p →¬q
- Aq →¬p
- Bq → p
- C¬q →¬p
- D¬q → p
9Find the contrapositive of ¬p → q .
- Aq →¬p
- B¬q → p
- Cp →¬q
- D¬q →¬p
10Find the bitwise OR of the bit strings 1011 0010 and 0110 0110.
- A0010 0011
- B0011 0011
- C1010 1001
- D1111 0110
11Find the bitwise AND of the bit strings 1010 1010 and 1001 1001.
- A1000 1000
- B0101 0101
- C1100 1100
- D0011 0011
12Find the bitwise XOR of the bit strings 0111 0101 and 1101 0101.
- A1111 0111
- B0101 0100
- C1010 0000
- D0110 1010
1313. Construct the truth table for the proposition (p→q)∨(¬p↔q)
- AT
T
F
T - BT
F
T
F - CT
T
T
T - DF
F
T
F
- AT
14Construct the truth table for the proposition p⊕(¬q→r).
- AF
F
F
T
T
T
T
F - BT
T
T
F
T
T
T
T - CT
F
T
F
T
F
T
F - DT
T
T
T
T
T
T
F
- AF
15Let p, q and r be the propositions “You get an A on the final exam”, “You do every exercise in this book” and “You get an A in this class” respectively. Write the proposition “Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class” using p, q and r and logical connectives.
- Ar→(p∧q)
- B(p∨q)→r
- C(p∧q)→r
- D¬r→(¬p∧¬q)
16Let p and q be the propositions “You get an A on the final exam” and “You get an A in this class” respectively. Write the proposition “To get an A in this class, it is necessary for you to get an A on the final” using p, q and logical connectives.
- Aq → p
- Bq ↔ p
- Cp → q
- Dp ⊕ q
1717. Evaluate the expression (1011⊕010)1∧110110
- A11 0100
- B11 0000
- C00 0110
- D11 1111
18Find the implication that is false.
- AIf 2 + 3 = 6, then God
- BIf 2 + 3 = 4, then 3 + 3 = 5.
- CIf pigs can fly, then 1 + 3 = 5
- DIf 2 + 3 = 5, then pigs can fly
19 Let p and q be the propositions “It is below freezing” and “It is snowing” respectively.
Express the proposition (p∨q)∧(p→¬q)as an English sentence.- AIt is below freezing or snowing, but it is not snowing only if it is below freezing.
- BIt is either below freezing or snowing, and it is not below freezing if it is snowing.
- CIt is either below freezing or it is snowing, but it is not snowing if it is below freezing.
- DIt is below freezing but not snowing.
20Let p and q be the propositions “You miss the final examination” and “You pass the course” respectively. Express the proposition ¬p ↔q as an English sentence.
- AThat you don’t miss the final examination is necessary for passing the course.
- BIf you don’t miss the final examination then you pass the course, and conversely.
- CMissing the final examination is sufficient for passing the course by you.
- DYou don’t miss the final examination or you pass the course.
21A compound proposition is a tautology if
- Ait is always false, no matter what the truth values of the propositions that occur in it.
- Bit is always true whenever each of the propositions that occur in it is true.
- Cit is always true, no matter what the truth values of the propositions that occur in it.
- Dit is always true whenever all the propositions that occur in it have the same truth values.
22The propositions p and q are logically equivalent if
- Ap ⊕ q is a tautology.
- B(p→q)∧(¬q→¬p)is a tautology.
- Cp ↔ q is a tautology.
- Dp ∨ q is a contradiction.
23Find the proposition that is a tautology.
- A(p→q)↔(¬q∨p)
- B¬(p∨q)↔(p∨q)
- C(p→q)↔(¬q→p)
- D¬(p∨q)↔(¬p∧¬q)
24Which of the following logical equivalences is a distributive law?
- Ap∨(q∨r)⇔(p∨q)∨r
- Bp∧(q∨r)⇔(p∧q)∨(p∧r)
- Cp∨q⇔q∨p
- Dp∧(q∧r)⇔p∧(q∧r)
25Find the proposition that is logically equivalent to p → q .
- A¬q ∨ p
- Bp ∨ q
- C¬p ∨ q
- D¬( p ∧q)
26Find the proposition that is logically equivalent to ¬p ∨¬q
- A¬( p ∨q)
- B(p→q)∨(q→p)
- C¬( p ∧q)
- D¬(p⊕q)
27A proposition is a contingency if
- Ait is both a tautology and a contradiction
- Bit is not a contradiction
- Cit is neither a tautology nor a contradiction
- Dit is not a tautology
28Find a compound proposition involving the propositions p, q and r that is true when p and q are false and r is true but is false otherwise.
- Ap ∨q ∨r
- B(¬p∧¬q)∨r
- C(p∧q)∨¬r
- D¬p∧¬q∧r
29Find a compound proposition involving the propositions p, q and r that is false when p is false and q and r are true, but is true otherwise.
- Ap∨¬q∨¬r
- B¬p∧q∧r
- Cp∧¬q∧¬r
- Dp→¬(q∧r)
30Find a compound proposition involving the propositions p, q and r that is true when p and q are true and r is false but is false otherwise.
- A(p∨¬r)∧(q∨¬r)
- B(p∨q)∧¬r
- Cp∧q∧¬r
- Dr→¬(p∧q)
31 Let P(x) be the statement “x spends less than three hours every weekday in class”, where the universe of discourse for x is the set of students. Express the proposition
“ ∃x¬P(x)” in English.- AEvery student doesn’t spend more than three hours every weekday in class.
- BThere is a student who doesn’t spend more than three hours every weekday in class.
- CThere is a student who spends no less than two hours every weekday in class
- DThere is a student who spends no less than three hours every weekday in class
32Let P(x, y) be the statement “x has taken y”, where the universe of discourse for x is the set of all students in your class and for y is the set of all computer courses at your
school. Express the proposition ∃y∀xP(x,y) in English.- AThere is a student at your class who has taken all computer courses at your school.
- BThere is a computer course at your school taken by all students in your class.
- CThere is a computer course at your school taken by at least one student in your class.
- DFor every student in your class there is a computer course at your school taken by him (or her).
33Let P(x) be the statement “x can speak Kazakh” and let Q(x) be the statement “x knows the computer language Delphi”, where the universe of discourse for x is the set of all students at your university. Express the sentence “There is a student at your university who can speak Kazakh but who doesn’t know Delphi” in terms of P(x), Q(x),
quantifiers and logical connectives.- A∃x(P(x)∨¬Q(x))
- B∃x(P(x)∧¬Q(x))
- C∀x(P(x)→¬Q(x))
- D∃x(Q(x)→P(x))
34Let S(x, y) be the statement “x + y = x ⋅ y”, where the universe of discourse for both variables is the set of integers. Which of the following statements is true?
- A∃x∃yS(x,y)
- B∀x∀y¬S(x,y)
- C∀x∃yS(x,y)
- D∀y∃xS(x,y)
35Let S(x, y) be the statement “x + 3y = 3x – y”, where the universe of discourse for both variables is the set of integers. Which of the following statements is true?
- A∀x∀y¬S(x,y)
- B∀x∃yS(x,y)
- C∀y∃xS(x,y)
- D∃x∀yS(x,y)
36Rewrite the statement ¬y∃∀xP(x,y) so that negations appear only within predicates
(that is, so that no negation is outside a quantifier or an expression involving logical connectives).- A∀y∀xP(x,y)
- B∃y∀x¬P(x,y)
- C∃x∀y¬P(x,y)
- D∀y∃x¬P(x,y)
37Rewrite the statement so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).
- A∃y(¬P(y)∨∃x¬S(x,y))
- B∀y(¬P(y)∧∀xS(x,y))
- C∀x(S(x,y)∧∃y¬P(y))
- D∃y(¬P(y)∧∀xS(x,y))
38Rewrite the statement so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).
- A∀y(∃x¬P(x,y)∧∀xR(,y))
- B∀y(∃x¬P(x,y)∨∀x¬R(x,y))
- C∃x(∀y¬P(x,y)∨∀y¬R(x,y))
- D∃y(∃x¬P(x,y)∨∀xR(x,y))
39Rewrite the statement so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives).
- A∃y(∀x∃z¬P(x,y,z)∧∃x∀z¬S(x,y,z))
- B∀y(∀x∃zPyx(,,)∧∃x∀zS(x,y,z))
- C∀x(∃y∃z¬P(x,y,z)∨∃y∀zS(x,y,z))
- D∃y(∀x∃zPyx(,,)∨∃x∀zS(x,y,z))
40Which of the following statements is true if the universe of discourse for all variables is the set of all integers?
- A∃n(n2 =8)
- B∀n∃m(n2+1<m−1)
- C∀n(n2 ≥1)
- D∃n∀m(n<m3)
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- Quiz on Untitled, created by aigerim Tumbaeva on 25/12/2019.
- Author
- aigerim Tumbaeva
- Language
- English
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- Created on 25 Dec 2019 · updated on 26 Dec 2019
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