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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?
- If p then q
- If q then p
- Both A and B
- 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 -
- If p then q
- If q then p
2. Conditional statement is also known as -?
- Negation
- Conjunction
- Disjunction
- Implication
Answer: D) Implication
Explanation:
Conditional statement is also known as implication.
3. Conditional statement is denoted by -?
- →
- ~
- ↔
- None
Answer: A) →
Explanation:
Conditional statement is denoted by →.
4. In implication p→q, p is known as -?
- Hypothesis
- Antecedent
- Both A and B
- 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 -?
- Conclusion
- Consequent
- Both A and B
- 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?
- True, true
- False, true
- False, false
- All of the above
Answer: D) All of the above
- If p is true and q is true, then p→q is true.
- If p is false and q is true, then p→q is true.
- If p is false and q is false, then p→q is true.
7. Which of the following is/are the conditional statement?
- If p=q and q=r, then p=r.
- If I get admission, then I will give exam.
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
The following are the conditional statements -
- If p=q and q=r, then p=r.
- If I get admission, then I will give exam.
8. What is/are the variation(s) in conditional statement?
- Contrapositive
- Converse
- Inverse
- All of the above
Answer: D) All of the above
Explanation:
The variations in conditional statement are -
- Contrapositive
- Converse
- Inverse
9. Contrapositive of p →q is the proposition ____?
- ~p→~q
- ~q→~p
- q→~p
- ~q→p
Answer: B) ~q→~p
Explanation:
Contrapositive of p →q is the proposition ~q→~p.
10. Converse of p →q is the proposition ___?
- ~q→p
- q→~p
- q→p
- ~q→~p
Answer: C) q→p
Explanation:
Converse of p →q is the proposition q→p.
11. Inverse of p →q is the proposition ___?
- p→~q
- ~p→q
- ~q→~p
- ~p→~q
Answer: D) ~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?
- p if and only if q
- q if and only if p
- Both A and B
- 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 -
- p if and only if q
- q if and only if p
13. Biconditional statement is also known as -?
- Equivalance
- Conjunction
- Disjunction
- Implication
Answer: D) Implication
Explanation:
Biconditional statement is also known as equivalance.
14. Biconditional statement is denoted by -?
- →
- ~
- ↔
- None
Answer: C) ↔
Explanation:
Biconditional statement is denoted by ↔.
15. If p is ___ and q is ___, then p↔q is false?
- 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 false.
- 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?
- Equivalent
- Duals
- Equals
- Same
Answer: B) Duals
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?
- AND and OR are dual of each other
- NAND and NOR are dual of each other
- In the event that any formula of the proposition holds true
- All of the above
Answer: D) All of the above
Explanation:
The following statements are TRUE -
- AND and OR are dual of each other
- NAND and NOR are dual of each other
- 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 _____?
- Analytically equivalent
- Logical
- Analytical
- Logically equivalent
Answer: D) 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)?
- p ∨ p≅p
- p ∧ p≅p
- Both A and B
- None of the above
Answer: C) Both A and B
Idempotent law is -
- p ∨ p≅p
- p ∧ p≅p
20. What is associative law?
- (p ∨ q) ∨ r ≅ p∨ (q ∨ r)
- p ∨ q ≅ q ∨ p
- p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)
- ¬¬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?
- p ∨ ¬p ≅ T
- ¬(p ∨ q) ≅ ¬p ∧ ¬q
- p ∨ q ≅ q ∨ p
- 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?
- p ∨ (q ∧ r) ≅ (p ∨ q) ∧ (p ∨ r)
- ¬(p ∨ q) ≅ ¬p ∧ ¬q
- ¬¬p ≅ p
- 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)?
- p ∨ F ≅ p
- p ∧ T≅ p
- p ∧ F≅F
- All of the above
Answer: D) All of the above
Identity laws are -
- p ∨ F ≅ p
- p ∧ T≅ p
- p ∧ F≅F
24. What is involution law?
- ¬(p ∨ q) ≅ ¬p ∧ ¬q
- p ∨ ¬p ≅ T
- ¬¬p ≅ p
- None of the above
Answer: C) ¬¬p ≅ p
Explanation:
Involution law is ¬¬p ≅ p.
25. What is/are complement law(s)?
- p ∨ ¬p ≅ T
- p ∧ ¬p ≅ T
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Complement laws are -
- p ∨ ¬p ≅ T
- p ∧ ¬p ≅ T
26. What is/are demorgan’s law(s)?
- ¬(p ∨ q) ≅ ¬p ∧ ¬q
- ¬(p ∧ q) ≅¬p ∨ ¬q
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Demorgan’s laws are -
- ¬(p ∨ q) ≅ ¬p ∧ ¬q
- ¬(p ∧ q) ≅¬p ∨ ¬q