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Unit 2: Logic Calculus - Practice Quiz

MTH136 — Discrete Structures 60 Questions
0 Correct 0 Wrong 60 Left
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1 What is the primary concern of the study of logic?

introduction to logic Easy
A. The measurement of physical quantities
B. The study of historical events and their causes over time
C. The classification of chemical compounds
D. The rules of valid reasoning and inference

2 Which of the following is a proposition?

propositions and compound propositions Easy
A. Please close the door
B. Wow, that is amazing!
C. The sun rises in the east
D. What is your name?

3 A compound proposition is formed by:

propositions and compound propositions Easy
A. Repeating the same word twice
B. Combining simple propositions using logical connectives
C. Adding numbers together
D. Writing a very long descriptive sentence that contains many clauses joined by commas

4 The logical operation represented by the symbol is:

basic logical operations (conjunction, disjunction, negation) Easy
A. Implication
B. Negation
C. Disjunction
D. Conjunction

5 The disjunction is false only when:

basic logical operations (conjunction, disjunction, negation) Easy
A. Both and are true
B. is false and is true
C. is true and is false
D. Both and are false

6 If is true, what is the value of ?

basic logical operations (conjunction, disjunction, negation) Easy
A. Both true and false
B. True
C. False
D. Undefined

7 The conjunction is true when:

basic logical operations (conjunction, disjunction, negation) Easy
A. At least one of or is true
B. Exactly one of or is true
C. Both and are false
D. Both and are true

8 A truth table for a compound proposition with distinct simple propositions has how many rows?

propositions and truth tables Easy
A.
B.
C.
D.

9 How many rows does the truth table of a proposition with 3 variables have?

propositions and truth tables Easy
A. 3
B. 6
C. 9
D. 8

10 What is the purpose of a truth table?

propositions and truth tables Easy
A. To count the number of variables
B. To solve algebraic equations
C. To arrange numbers in ascending order
D. To list all possible truth values of a proposition for every combination of inputs

11 A proposition that is always true regardless of the truth values of its components is called a:

tautologies and contradiction Easy
A. Contradiction
B. Tautology
C. Disjunction
D. Contingency

12 A proposition that is always false is called a:

tautologies and contradiction Easy
A. Tautology
B. Conjunction
C. Contingency
D. Contradiction

13 Which of the following is a tautology?

tautologies and contradiction Easy
A.
B.
C.
D.

14 The expression is an example of a:

tautologies and contradiction Easy
A. Biconditional
B. Tautology
C. Contradiction
D. Contingency

15 Two propositions are logically equivalent when:

logical equivalence Easy
A. They contain the same number of variables
B. They are both compound propositions
C. They have the same truth value in every possible case
D. They use the same logical connective at least once somewhere in the expression

16 According to De Morgan's law, is equivalent to:

logical equivalence Easy
A.
B.
C.
D.

17 Which symbol is commonly used to denote logical equivalence?

logical equivalence Easy
A.
B.
C.
D.

18 The conditional statement is false only when:

conditional and biconditional statements Easy
A. is false and is true
B. Both and are false
C. Both and are true
D. is true and is false

19 The biconditional is true when:

conditional and biconditional statements Easy
A. is always false
B. and have different truth values
C. and have the same truth value
D. is always true

20 In the conditional statement , the proposition is called the:

conditional and biconditional statements Easy
A. Contradiction
B. Consequent
C. Conclusion
D. Hypothesis

21 Which of the following sentences is a proposition?

propositions and compound propositions Medium
A. Please close the door before you leave the room.
B.
C. Solve the equation
D. What time is it right now?

22 If is true and is false, what is the truth value of ?

basic logical operations (conjunction, disjunction, negation) Medium
A. Cannot be determined
B. Depends on additional variables
C. True
D. False

23 The conditional statement is false only when:

conditional and biconditional statements Medium
A. is true and is false
B. is false and is true
C. Both and are false
D. Both and are true

24 Which statement is logically equivalent to ?

logical equivalence Medium
A.
B.
C.
D.

25 Which of the following is a tautology?

tautologies and contradiction Medium
A.
B.
C.
D.

26 A compound proposition that is always false for every possible assignment of truth values to its variables is called a:

tautologies and contradiction Medium
A. Contingency
B. Tautology
C. Biconditional
D. Contradiction

27 What is the contrapositive of the statement "If it rains, then the ground is wet"?

conditional and biconditional statements Medium
A. If it does not rain, then the ground is not wet
B. If the ground is not wet, then it does not rain
C. If it rains, then the ground is not wet
D. If the ground is wet, then it rains

28 The negation of the statement "All students passed the exam" is:

basic logical operations (conjunction, disjunction, negation) Medium
A. At least one student did not pass the exam
B. All students failed the exam
C. No students passed the exam
D. Some students passed the exam

29 How many rows are required in a truth table for a compound proposition containing 4 distinct propositional variables?

propositions and truth tables Medium
A.
B.
C.
D.

30 According to De Morgan's Law, is equivalent to:

logical equivalence Medium
A.
B.
C.
D.

31 The biconditional is true when:

conditional and biconditional statements Medium
A. and have opposite truth values
B. Both and are false only
C. and have the same truth value
D. At least one of , is true

32 Which expression is the converse of ?

logical equivalence Medium
A.
B.
C.
D.

33 If is true, which of the following must also be true?

basic logical operations (conjunction, disjunction, negation) Medium
A.
B.
C.
D.

34 For the expression , if this whole expression is true, what can be concluded about ?

propositions and truth tables Medium
A. is undefined
B. is false
C. can be either true or false
D. is true

35 In propositional logic, which of the following best describes a compound proposition?

introduction to logic Medium
A. A sentence that cannot be assigned a truth value
B. A proposition formed by combining one or more propositions using logical connectives
C. A proposition that is always true
D. A proposition containing exactly one variable

36 The expression is a:

tautologies and contradiction Medium
A. Contradiction
B. Contingency
C. Tautology
D. Neither, it is invalid

37 Which of the following pairs are logically equivalent?

logical equivalence Medium
A. and
B. and
C. and
D. and

38 In the truth table of (exclusive or), the result is true in how many of the four rows?

propositions and truth tables Medium
A. rows
B. rows
C. rows
D. row

39 The statement " if and only if " can be expressed as which combination of conditionals?

conditional and biconditional statements Medium
A.
B.
C.
D.

40 Consider the sentence: "This statement is false." Why is it not a proposition?

introduction to logic Medium
A. It cannot be consistently assigned a single truth value of true or false because it refers to itself and creates a paradox
B. It is written in the imperative mood
C. It is grammatically incorrect
D. It contains no logical connectives

41 Which of the following is logically equivalent to ?

logical equivalence Hard
A.
B.
C.
D.

42 For which values is true?

tautologies and contradiction Hard
A. Only when both and are false
B. Only when both and are true
C. For all truth assignments
D. Whenever holds

43 The statement is logically equivalent to:

conditional and biconditional statements Hard
A.
B.
C.
D.

44 Which expression is NOT logically equivalent to the other three?

logical equivalence Hard
A.
B.
C.
D.

45 A compound proposition built from distinct propositional variables. How many rows does its complete truth table have, and how many distinct such propositions exist (up to equivalence)?

propositions and truth tables Hard
A. rows and propositions
B. rows and propositions
C. rows and propositions
D. rows and propositions

46 The NAND operation is functionally complete. Which expression using only NAND is equivalent to ?

basic logical operations (conjunction, disjunction, negation) Hard
A.
B.
C.
D.

47 Which of the following is a tautology?

tautologies and contradiction Hard
A.
B.
C.
D.

48 Simplify to its minimal equivalent form.

logical equivalence Hard
A.
B.
C.
D.

49 The biconditional is logically equivalent to which of the following?

conditional and biconditional statements Hard
A.
B.
C.
D.

50 Consider Why is not a proposition?

propositions and compound propositions Hard
A. It depends on an unknown variable
B. It cannot be consistently assigned a single truth value
C. It is grammatically incorrect
D. It contains no logical connectives

51 How many of the rows make true?

tautologies and contradiction Hard
A. 6 rows
B. 8 rows
C. 4 rows
D. 5 rows

52 Using the absorption and distributive laws, simplify .

logical equivalence Hard
A.
B.
C.
D.

53 The exclusive-or satisfies which associativity/self-inverse property useful in parity checking?

basic logical operations (conjunction, disjunction, negation) Hard
A. and
B. and
C. and
D. and

54 Which statement correctly relates a conditional, its converse, inverse, and contrapositive?

conditional and biconditional statements Hard
A. A conditional is equivalent to its converse; the inverse is equivalent to the contrapositive
B. All four are always logically equivalent
C. A conditional is equivalent to its contrapositive; the converse is equivalent to the inverse
D. A conditional is equivalent to its inverse only

55 Which pair of formulas is NOT logically equivalent?

logical equivalence Hard
A. and
B. and
C. and vs and
D. and

56 A truth function on 2 variables outputs T in exactly 3 of 4 rows and F when both inputs are false. Which connective is it?

propositions and truth tables Hard
A.
B.
C.
D.

57 Which formula is a contradiction (false under every assignment)?

tautologies and contradiction Hard
A.
B.
C.
D.

58 Given the argument: premises and , conclusion . This valid inference rule is called:

conditional and biconditional statements Hard
A. Modus tollens
B. Disjunctive syllogism
C. Constructive dilemma
D. Modus ponens

59 Which set of connectives is functionally complete (able to express every truth function)?

basic logical operations (conjunction, disjunction, negation) Hard
A.
B.
C.
D.

60 Prove or disprove: is logically equivalent to . Which is correct?

logical equivalence Hard
A. They are NOT equivalent; they differ only when
B. They are NOT equivalent; they differ when
C. They are equivalent by the exportation law
D. They are equivalent because both reduce to
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