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Discrete Mathematics | Basic Logical Operations MCQs
Discrete Mathematics | Basic Logical Operations MCQs: This section contains multiple-choice questions and answers on Basic Logical Operations in Discrete Mathematics.
Submitted by Anushree Goswami, on July 18, 2022
1. Which of the following is/are basic logical operation(s)?
- Negation
- Conjunction
- Disjunction
- All of the above
Answer: D) All of the above
Explanation:
The following are basic logical operation - Negation, Conjunction, Disjunction, etc.
2. _____ refers to the opposite of what was originally stated?
- Negation
- Conjunction
- Disjunction
- Implication
Answer: A) Negation
Explanation:
Negation refers to the opposite of what was originally stated.
3. Assume that p represents a statement. The negation of p will be denoted by __?
- -p
- ~p
- !p
- *p
Answer: B) ~p
Explanation:
Assume that p represents a statement. The negation of p will be denoted by ~p.
4. ~p is read as -?
- it is the case that p
- case that p
- it is not the case that p
- p
Answer: C) it is not the case that p
Explanation:
~p is read as it is not the case that p.
5. If p is ____, then ~p will be ____?
- True, false
- False, true
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
If p is true, then ~p will be false and vice-versa.
6. An Anding of two statements is a ____?
- Negation
- Conjunction
- Disjunction
- Implication
Answer: B) Conjunction
An Anding of two statements is a conjunction.
7. "____" is a compound statement if p and q are two statements in case of conjunction?
- p or q
- p and q
- p with q
- p for q
Answer: B) p and q
Explanation:
"p and q" is a compound statement if p and q are two statements in case of conjunction.
8. In case of conjunction, compound statement p and q is denoted by -?
- p ∧ q
- p - q
- p + q
- p * q
Answer: A) p ∧ q
Explanation:
In case of conjunction, compound statement p and q is denoted by p ∧ q.
9. If both p and q are true, then only conjunction of p and q is ___?
- True
- False
- Null
- None
Answer: A) True
Explanation:
If both p and q are true, then only conjunction of p and q is true.
10. An Oring of two statements is a ____?
- Conjunction
- Disjunction
- Implication
- Negation
Answer: B) Disjunction
Explanation:
An Oring of two statements is a Disjunction.
11. "_____" is a compound statement if p and q are two statements in case of disjunction?
- p and q
- p for q
- p from q
- p or q
Answer: D) p or q
Explanation:
"p or q" is a compound statement if p and q are two statements in case of disjunction.
12. In case of disjunction, compound statement p and q is denoted by -?
- p ∧ q
- p - q
- p + q
- p ∨ q
Answer: D) p ∨ q
Explanation:
In case of disjunction, compound statement p and q is denoted by p ∨ q.
13. It is true that p and q are disjunctive if at least ___ of them is true, and it is false if both are false?
- One
- Two
- Both
- None
Answer: A) One
Explanation:
It is true that p and q are disjunctive if at least one of them is true, and it is false if both are false.
14. If p is true and q is false, then p ∨ q is -?
- True
- False
- Null
- None
Answer: A) True
Explanation:
If p is true and q is false, then p ∨ q is true.
15. If p is true and q is false, then p ∧ q is -?
- True
- False
- Null
- None
Answer: B) False
Explanation:
If p is true and q is false, then p ∧ q is false.
16. An implication p⟶q is the proposition "____."?
- p and q
- p or q
- If q, then p
- If p, then q
Answer: D) If p, then q
Explanation:
An implication p⟶q is the proposition "if p, then q."
17. When p is ___ and q is ____, p⟶q is false?
- True, true
- True, false
- False, true
- False, false
Answer: B) True, false
Explanation:
When p is true and q is false, p⟶q is false.
18. p ↔ q is a bi-conditional logical connective which is true when p and q are the ____?
- True, true
- False, false
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
p ↔ q is a bi-conditional logical connective which is true when p and q are the same.
19. Which of the following is/are the derived connector(s)?
- NAND
- NOR
- XOR
- All of the above
Answer: D) All of the above
Explanation:
The following are the derived connectors -
- NAND
- NOR
- XOR
20. An AND followed by a ____ is called a NAND?
- Negation
- Conjunction
- Disjunction
- Implication
Answer: A) Negation
Explanation:
An AND followed by a negation is called a NAND.
21. NAND of p and q is denoted by -?
- p ↑ q
- p ↓ q
- p ⨁ q
- None
Answer: A) p ↑ q
Explanation:
NAND of p and q is denoted by p ↑ q.
22. If p is ____ and q is ___, then p ↑ q is false?
- True, true
- False, true
- True, false
- False, false
Answer: A) True, true
Explanation:
If p is true and q is true, then p ↑ q is false.
23. If p is ____ and q is ___, then p ↑ q is true?
- False, false
- False, true
- True, false
- All of the above
Answer: D) All of the above
Explanation:
- If p is false and q is false, then p ↑ q is true.
- If p is false and q is true, then p ↑ q is true.
- If p is true and q is false, then p ↑ q is true.
24. What is NOR also known as?
- Denial
- Joint
- Joint Denial
- None
Answer: C) Joint Denial
Explanation:
NOR is also known as Joint Denial.
25. An OR followed by a ____ is called a NOR?
- Negation
- Conjunction
- Disjunction
- Implication
Answer: A) Negation
Explanation:
An OR followed by a negation is called a NOR.
26. NOR of p and q is denoted by -?
- p ↑ q
- p ↓ q
- p ⨁ q
- None
Answer: B) p ↓ q
Explanation:
NOR of p and q is denoted by p ↓ q.
27. If p is ____ and q is ___, then p ↓ q is true?
- True, true
- False, true
- True, false
- False, false
Answer: D) False, false
Explanation:
If p is false and q is false, then p ↓ q is true.
28. If p is ____ and q is ___, then p ↓ q is false?
- True, true
- False, true
- True, false
- All of the above
Answer: D) All of the above
Explanation:
- If p is true and q is true, then p ↓ q is false.
- If p is false and q is true, then p ↓ q is false.
- If p is true and q is false, then p ↓ q is false.
29. XOR of p and q is denoted by -?
- p ↑ q
- p ↓ q
- p ⨁ q
- None
Answer: C) p ⨁ q
Explanation:
XOR of p and q is denoted by p ⨁ q.
30. If p is ____ and q is ___, then p ⨁ q is false?
- True, true
- False, false
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
- If p is true and q is true, then p ⨁ q is false.
- If p is false and q is false, then p ⨁ q is false.
31. If p is ____ and q is ___, then p ⨁ q is true?
- True, false
- False, true
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
- If p is true and q is false, then p ⨁ q is true.
- If p is false and q is true, then p ⨁ q is true.