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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.

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