Discrete Structures Multiple Choice Questions Worksheet

Description

21 Discrete structures questions which includes true or false questions and multiple choice questions. The attached file contains the questions.

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

Section I: True (T) or False (F) – Circle Your Answer
1. Propositional well-formed formula may be proven true with an algorithm same as a predicate
well-formed formula may be proven valid.
a. True
b. False
2. The key to a proof by the first principle of induction is to see how the truth of P at the value
k + 1 depends on the truth of P at value k.
a. True
b. False
3. Recursive algorithms are valuable primarily because they run more efficiently than iterative
algorithms.
a. True
b. False
4. The predicate quantifier, , indicates that there exists 1, a few or some objects in the
domain.
a. True
b. False
5. Modus Ponens is probably the most intuitive inference rule.
a. True
b. False
6. Is the following expression true or false? (D U B’)’ = D’ ꓵ B
a. True
b. False
7. Given the truth values A (true), B (true), C (false), D (True) what is the truth value of the
following wff? (A’ V B’) Λ (C’ Λ A) → D
a. True
b. False
8. The expression: A’ → (B V C’) is a tautology.
a. True
b. False
9. A recurrence relation is homogenous if g(n) has a constant coefficient.
a. True
b. False
10. Your professor has 4 pairs of shoes, 12 pairs of socks, 10 pairs of pants, 15 different shirts, 5 suit
jackets and 3 “UTA” lapel pins he may or may not pin to his jacket. Given these options, he
therefore has 108,000 different combinations he may wear.
a. True
b. False
11. The following expression is a well-formed formula: ((A V B) Λ C) → (B V C’))
a. True
b. False
12. The disjunction of any propositional wff with a tautology has a truth value of true.
a. True
b. False
13. (A Λ B) Λ C Λ D → E → F ↔ A Λ B Λ C Λ D Λ E → F
a. True
b. False
Section II: Multiple Choice – Select the best answer by circling your answer
14. ________ is the justification for step 4 in the following proof sequence?
a. Modus Tollens
b. Modus Ponens
c. Contraposition
d. Hypothetical Syllogism
e. None of the above
Proof: 1. A’
2. B
3. B→ (A V C)
4. A V C
15. Which of the following results is a counter example for the following statement: if n is an even
integer, then n2-1 is an odd integer.
a. 3
b. 15
c. 8
d. 35
e. None of the above
16. The number of elements in set C is which of the following:
|C| = |A  B’| – |A  B|, Where A and B are subsets of super set S, and
S = {j, k, l, m, n, o, 1, 3, 5, 7, !) A = {k, m, n, 1, 5, 7}
B = {n, o, 1, 3, 5, !)
a. 11
b. 6
c. 12
d. 5
e. 3
17. What is the justification for the following statement?
a. Implication
b. DeMorgan’s Law
c. Modus Tollens
d. Modus Ponens
e. None of the above
Statement:
If the business declares bankruptcy, then all assets must be confiscated. The
business declared bankruptcy. It follows that all assets must be confiscated.
18. Select the predicate expression that is equivalent to “Not every mystery is a spy novel” given the
following: Note: the Domain is the whole world
S(x): x is a spy novel
a.
b.
c.
d.
e.
L(x): x is long
M(x): x is a mystery
B(x,y): x is better than y
(x)(M(x) Λ [S(x)]’)
(y)(x)(S(x))’
(y)(S(x))’ Λ M(x)
(x)(M(x) Λ [S(x)])’
None of the above
19. The elements of the set describe by the following statement is/are: {x│x  N and x2 – 5x + 6 = 0}
a. {-2, -3, 2, 3}
b. {-2, -3}
c. {2, 3}
d. {-2, -3, 0, 2, 3)
e. None of the above
20. Which of the following statements is true?
a.   A
b. {} = {{}}
c. If A  B and B  C, then A  C
d. If A ≠ B and B ≠ C, then A ≠ C
e. If A B and B  C, then A C
For the following questions show all work for partial credit.
21. Let A = {2, 4, 5, 6, 8}, B = {1, 4, 5, 9}, C = {x | x ε Domain Z and 2 =1 (Partial Credit Possible)
Section I: True (T) or False (F) – Circle Your Answer
1. Propositional well-formed formula may be proven true with an algorithm same as a predicate
well-formed formula may be proven valid.
a. True
b. False
2. The key to a proof by the first principle of induction is to see how the truth of P at the value
k + 1 depends on the truth of P at value k.
a. True
b. False
3. Recursive algorithms are valuable primarily because they run more efficiently than iterative
algorithms.
a. True
b. False
4. The predicate quantifier, , indicates that there exists 1, a few or some objects in the
domain.
a. True
b. False
5. Modus Ponens is probably the most intuitive inference rule.
a. True
b. False
6. Is the following expression true or false? (D U B’)’ = D’ ꓵ B
a. True
b. False
7. Given the truth values A (true), B (true), C (false), D (True) what is the truth value of the
following wff? (A’ V B’) Λ (C’ Λ A) → D
a. True
b. False
8. The expression: A’ → (B V C’) is a tautology.
a. True
b. False
9. A recurrence relation is homogenous if g(n) has a constant coefficient.
a. True
b. False
10. Your professor has 4 pairs of shoes, 12 pairs of socks, 10 pairs of pants, 15 different shirts, 5 suit
jackets and 3 “UTA” lapel pins he may or may not pin to his jacket. Given these options, he
therefore has 108,000 different combinations he may wear.
a. True
b. False
11. The following expression is a well-formed formula: ((A V B) Λ C) → (B V C’))
a. True
b. False
12. The disjunction of any propositional wff with a tautology has a truth value of true.
a. True
b. False
13. (A Λ B) Λ C Λ D → E → F ↔ A Λ B Λ C Λ D Λ E → F
a. True
b. False
Section II: Multiple Choice – Select the best answer by circling your answer
14. ________ is the justification for step 4 in the following proof sequence?
a. Modus Tollens
b. Modus Ponens
c. Contraposition
d. Hypothetical Syllogism
e. None of the above
Proof: 1. A’
2. B
3. B→ (A V C)
4. A V C
15. Which of the following results is a counter example for the following statement: if n is an even
integer, then n2-1 is an odd integer.
a. 3
b. 15
c. 8
d. 35
e. None of the above
16. The number of elements in set C is which of the following:
|C| = |A  B’| – |A  B|, Where A and B are subsets of super set S, and
S = {j, k, l, m, n, o, 1, 3, 5, 7, !) A = {k, m, n, 1, 5, 7}
B = {n, o, 1, 3, 5, !)
a. 11
b. 6
c. 12
d. 5
e. 3
17. What is the justification for the following statement?
a. Implication
b. DeMorgan’s Law
c. Modus Tollens
d. Modus Ponens
e. None of the above
Statement:
If the business declares bankruptcy, then all assets must be confiscated. The
business declared bankruptcy. It follows that all assets must be confiscated.
18. Select the predicate expression that is equivalent to “Not every mystery is a spy novel” given the
following: Note: the Domain is the whole world
S(x): x is a spy novel
a.
b.
c.
d.
e.
L(x): x is long
M(x): x is a mystery
B(x,y): x is better than y
(x)(M(x) Λ [S(x)]’)
(y)(x)(S(x))’
(y)(S(x))’ Λ M(x)
(x)(M(x) Λ [S(x)])’
None of the above
19. The elements of the set describe by the following statement is/are: {x│x  N and x2 – 5x + 6 = 0}
a. {-2, -3, 2, 3}
b. {-2, -3}
c. {2, 3}
d. {-2, -3, 0, 2, 3)
e. None of the above
20. Which of the following statements is true?
a.   A
b. {} = {{}}
c. If A  B and B  C, then A  C
d. If A ≠ B and B ≠ C, then A ≠ C
e. If A B and B  C, then A C
For the following questions show all work for partial credit.
21. Let A = {2, 4, 5, 6, 8}, B = {1, 4, 5, 9}, C = {x | x ε Domain Z and 2

Purchase answer to see full
attachment

Tags:
Modus Ponens

Recursive Algorithms

principle of induction

Predicate well formed formula

Predicate quantifier

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.