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# Discrete Mathematics | Conditional and Biconditional Statements MCQs

Discrete Mathematics | Conditional and Biconditional Statements MCQs: This section contains multiple-choice questions and answers on Conditional and Biconditional Statements in Discrete Mathematics.
Submitted by Anushree Goswami, on July 18, 2022

1. What is/are the meaning of conditional statement when there are two statements p and q?

1. If p then q
2. If q then p
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The meaning of conditional statement when there are two statements p and q are -

1. If p then q
2. If q then p

2. Conditional statement is also known as -?

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

Explanation:

Conditional statement is also known as implication.

3. Conditional statement is denoted by -?

1. ~
2. None

Explanation:

Conditional statement is denoted by →.

4. In implication p→q, p is known as -?

1. Hypothesis
2. Antecedent
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

In implication p→q, p is known as hypothesis or antecedent.

5. In implication p→q, q is known as -?

1. Conclusion
2. Consequent
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

In implication p→q, q is known as conclusion or consequent.

6. If p is ____ and q is ____, then p→q is true?

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

Answer: D) All of the above

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

7. Which of the following is/are the conditional statement?

1. If p=q and q=r, then p=r.
2. If I get admission, then I will give exam.
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The following are the conditional statements -

1. If p=q and q=r, then p=r.
2. If I get admission, then I will give exam.

8. What is/are the variation(s) in conditional statement?

1. Contrapositive
2. Converse
3. Inverse
4. All of the above

Answer: D) All of the above

Explanation:

The variations in conditional statement are -

1. Contrapositive
2. Converse
3. Inverse

9. Contrapositive of p →q is the proposition ____?

1. ~p→~q
2. ~q→~p
3. q→~p
4. ~q→p

Explanation:

Contrapositive of p →q is the proposition ~q→~p.

10. Converse of p →q is the proposition ___?

1. ~q→p
2. q→~p
3. q→p
4. ~q→~p

Explanation:

Converse of p →q is the proposition q→p.

11. Inverse of p →q is the proposition ___?

1. p→~q
2. ~p→q
3. ~q→~p
4. ~p→~q

Explanation:

Inverse of p →q is the proposition ~p→~q.

12. What is/are the meaning of biconditional statement when there are two statements p and q?

1. p if and only if q
2. q if and only if p
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

The meaning of biconditional statement when there are two statements p and q are -

1. p if and only if q
2. q if and only if p

13. Biconditional statement is also known as -?

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

Explanation:

Biconditional statement is also known as equivalance.

14. Biconditional statement is denoted by -?

1. ~
2. None

Explanation:

Biconditional statement is denoted by ↔.

15. If p is ___ and q is ___, then p↔q is false?

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 false.
2. If p is false and q is true, then p↔q is false.

16. By substituting ∧ (AND) by ∨ (OR) by ∧ (AND), two formulas A1 and A2 become ___ of each other?

1. Equivalent
2. Duals
3. Equals
4. Same

Explanation:

By substituting ∧ (AND) by ∨ (OR) by ∧ (AND), two formulas A1 and A2 become duals of each other.

17. Which of the following statement(s) is/are TRUE?

1. AND and OR are dual of each other
2. NAND and NOR are dual of each other
3. In the event that any formula of the proposition holds true
4. All of the above

Answer: D) All of the above

Explanation:

The following statements are TRUE -

1. AND and OR are dual of each other
2. NAND and NOR are dual of each other
3. In the event that any formula of the proposition holds true

18. When two propositions have exactly the same truth values regardless of circumstance, they are said to be _____?

1. Analytically equivalent
2. Logical
3. Analytical
4. Logically equivalent

Explanation:

When two propositions have exactly the same truth values regardless of circumstance, they are said to be logically equivalent.

19. What is/are idempotent law(s)?

1. p ∨ p≅p
2. p ∧ p≅p
3. Both A and B
4. None of the above

Answer: C) Both A and B

Idempotent law is -

1. p ∨ p≅p
2. p ∧ p≅p

20. What is associative law?

1. (p ∨ q) ∨ r ≅ p∨ (q ∨ r)
2. p ∨ q ≅ q ∨ p
3. p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)
4. ¬¬p ≅ p

Answer: A) (p ∨ q) ∨ r ≅ p∨ (q ∨ r)

Explanation:

Associative law is (p ∨ q) ∨ r ≅ p∨ (q ∨ r).

21. What is commutative law?

1. p ∨ ¬p ≅ T
2. ¬(p ∨ q) ≅ ¬p ∧ ¬q
3. p ∨ q ≅ q ∨ p
4. p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)

Answer: C) p ∨ q ≅ q ∨ p

Explanation:

Commutative law is p ∨ q ≅ q ∨ p.

22. What is distributive law?

1. p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)
2. ¬(p ∨ q) ≅ ¬p ∧ ¬q
3. ¬¬p ≅ p
4. p ∨ F ≅ p

Answer: A) p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)

Explanation:

Distributive law is p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r).

23. What is/are identity law(s)?

1. p ∨ F ≅ p
2. p ∧ T≅ p
3. p ∧ F≅F
4. All of the above

Answer: D) All of the above

Identity laws are -

1. p ∨ F ≅ p
2. p ∧ T≅ p
3. p ∧ F≅F

24. What is involution law?

1. ¬(p ∨ q) ≅ ¬p ∧ ¬q
2. p ∨ ¬p ≅ T
3. ¬¬p ≅ p
4. None of the above

Explanation:

Involution law is ¬¬p ≅ p.

25. What is/are complement law(s)?

1. p ∨ ¬p ≅ T
2. p ∧ ¬p ≅ T
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Complement laws are -

1. p ∨ ¬p ≅ T
2. p ∧ ¬p ≅ T

26. What is/are demorgan’s law(s)?

1. ¬(p ∨ q) ≅ ¬p ∧ ¬q
2. ¬(p ∧ q) ≅¬p ∨ ¬q
3. Both A and B
4. None of the above

Answer: C) Both A and B

Explanation:

Demorgan’s laws are -

1. ¬(p ∨ q) ≅ ¬p ∧ ¬q
2. ¬(p ∧ q) ≅¬p ∨ ¬q