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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)?

1. Negation
2. Conjunction
3. Disjunction
4. All of the above

Answer: D) All of the above

Explanation:

The following are basic logical operation - Negation, Conjunction, Disjunction, etc.

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2. _____ refers to the opposite of what was originally stated?

1. Negation
2. Conjunction
3. Disjunction
4. Implication

Answer: A) Negation

Explanation:

Negation refers to the opposite of what was originally stated.

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3. Assume that p represents a statement. The negation of p will be denoted by __?

1. -p
2. ~p
3. !p
4. *p

Answer: B) ~p

Explanation:

Assume that p represents a statement. The negation of p will be denoted by ~p.

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4. ~p is read as -?

1. it is the case that p
2. case that p
3. it is not the case that p
4. p

Answer: C) it is not the case that p

Explanation:

~p is read as it is not the case that p.

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5. If p is ____, then ~p will be ____?

1. True, false
2. False, true
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

If p is true, then ~p will be false and vice-versa.

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6. An Anding of two statements is a ____?

1. Negation
2. Conjunction
3. Disjunction
4. Implication

Answer: B) Conjunction

An Anding of two statements is a conjunction.

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7. "____" is a compound statement if p and q are two statements in case of conjunction?

1. p or q
2. p and q
3. p with q
4. 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.

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8. In case of conjunction, compound statement p and q is denoted by -?

1. p ∧ q
2. p - q
3. p + q
4. p * q

Answer: A) p ∧ q

Explanation:

In case of conjunction, compound statement p and q is denoted by p ∧ q.

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9. If both p and q are true, then only conjunction of p and q is ___?

1. True
2. False
3. Null
4. None

Answer: A) True

Explanation:

If both p and q are true, then only conjunction of p and q is true.

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10. An Oring of two statements is a ____?

1. Conjunction
2. Disjunction
3. Implication
4. Negation

Answer: B) Disjunction

Explanation:

An Oring of two statements is a Disjunction.

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11. "_____" is a compound statement if p and q are two statements in case of disjunction?

1. p and q
2. p for q
3. p from q
4. 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.

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12. In case of disjunction, compound statement p and q is denoted by -?

1. p ∧ q
2. p - q
3. p + q
4. p ∨ q

Answer: D) p ∨ q

Explanation:

In case of disjunction, compound statement p and q is denoted by p ∨ q.

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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?

1. One
2. Two
3. Both
4. 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.

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14. If p is true and q is false, then p ∨ q is -?

1. True
2. False
3. Null
4. None

Answer: A) True

Explanation:

If p is true and q is false, then p ∨ q is true.

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15. If p is true and q is false, then p ∧ q is -?

1. True
2. False
3. Null
4. None

Answer: B) False

Explanation:

If p is true and q is false, then p ∧ q is false.

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16. An implication p⟶q is the proposition "____."?

1. p and q
2. p or q
3. If q, then p
4. If p, then q

Answer: D) If p, then q

Explanation:

An implication p⟶q is the proposition "if p, then q."

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17. When p is ___ and q is ____, p⟶q is false?

1. True, true
2. True, false
3. False, true
4. False, false

Answer: B) True, false

Explanation:

When p is true and q is false, p⟶q is false.

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18. p ↔ q is a bi-conditional logical connective which is true when p and q are the ____?

1. True, true
2. False, false
3. Both A and B
4. 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.

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19. Which of the following is/are the derived connector(s)?

1. NAND
2. NOR
3. XOR
4. All of the above

Answer: D) All of the above

Explanation:

The following are the derived connectors -

1. NAND
2. NOR
3. XOR

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20. An AND followed by a ____ is called a NAND?

1. Negation
2. Conjunction
3. Disjunction
4. Implication

Answer: A) Negation

Explanation:

An AND followed by a negation is called a NAND.

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21. NAND of p and q is denoted by -?

1. p ↑ q
2. p ↓ q
3. p ⨁ q
4. None

Answer: A) p ↑ q

Explanation:

NAND of p and q is denoted by p ↑ q.

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22. If p is ____ and q is ___, then p ↑ q is false?

1. True, true
2. False, true
3. True, false
4. False, false

Answer: A) True, true

Explanation:

If p is true and q is true, then p ↑ q is false.

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23. If p is ____ and q is ___, then p ↑ q is true?

1. False, false
2. False, true
3. True, false
4. All of the above

Answer: D) All of the above

Explanation:

1. If p is false and q is false, then p ↑ q is true.
2. If p is false and q is true, then p ↑ q is true.
3. If p is true and q is false, then p ↑ q is true.

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24. What is NOR also known as?

1. Denial
2. Joint
3. Joint Denial
4. None

Answer: C) Joint Denial

Explanation:

NOR is also known as Joint Denial.

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25. An OR followed by a ____ is called a NOR?

1. Negation
2. Conjunction
3. Disjunction
4. Implication

Answer: A) Negation

Explanation:

An OR followed by a negation is called a NOR.

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26. NOR of p and q is denoted by -?

1. p ↑ q
2. p ↓ q
3. p ⨁ q
4. None

Answer: B) p ↓ q

Explanation:

NOR of p and q is denoted by p ↓ q.

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27. If p is ____ and q is ___, then p ↓ q is true?

1. True, true
2. False, true
3. True, false
4. False, false

Answer: D) False, false

Explanation:

If p is false and q is false, then p ↓ q is true.

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28. If p is ____ and q is ___, then p ↓ q is false?

1. True, true
2. False, true
3. True, false
4. All of the above

Answer: D) All of the above

Explanation:

1. If p is true and q is true, then p ↓ q is false.
2. If p is false and q is true, then p ↓ q is false.
3. If p is true and q is false, then p ↓ q is false.

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29. XOR of p and q is denoted by -?

1. p ↑ q
2. p ↓ q
3. p ⨁ q
4. None

Answer: C) p ⨁ q

Explanation:

XOR of p and q is denoted by p ⨁ q.

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30. If p is ____ and q is ___, then p ⨁ q is false?

1. True, true
2. False, false
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

1. If p is true and q is true, then p ⨁ q is false.
2. If p is false and q is false, then p ⨁ q is false.

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31. If p is ____ and q is ___, then p ⨁ q is true?

1. True, false
2. False, true
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

1. If p is true and q is false, then p ⨁ q is true.
2. If p is false and q is true, then p ⨁ q is true.

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