Q1: 1. If p → q is false and q → r is true, then which of the following is true?

• A) p → r
• B) p ↔ r
• C) ¬p → r
• D) p ∨ r

Q2: 2. Which of the following is equivalent to ¬(p ∧ q)?

• A) ¬p ∨ ¬q
• B) ¬p ∧ ¬q
• C) p ∨ q
• D) p ∧ q

Q3: 3. If p → (q ∧ r) is true, and q is false, then which of the following is true?

• A) p is true
• B) r is false
• C) p is false
• D) r is true

Q4: 4. What is the contrapositive of the statement "If it is a weekend, then the store is crowded"?

• A) If the store is not crowded, then it is not a weekend.
• B) If the store is crowded, then it is a weekend.
• C) If it is not a weekend, then the store is crowded.
• D) If the store is crowded, then it is not a weekend.

Q5: 5. Which of the following is the contrapositive of the statement "If it is summer, then it is hot"?

• A) If it is not hot, then it is not summer.
• B) If it is hot, then it is summer.
• C) If it is not summer, then it is not hot.
• D) If it is hot, then it is not summer.

Q6: 6. If p ∨ q is true, and ¬q is true, then which of the following is true?

• A) p is true
• B) q is false
• C) p is false
• D) ¬p is true

Q7: 7. Which of the following is the negation of the statement "If it is Monday, then it is a school day"?

• A) It is Monday and it is not a school day.
• B) It is not Monday or it is a school day.
• C) It is not Monday and it is not a school day.
• D) It is Monday or it is not a school day.

Q8: 8. If p ↔ q is true, then which of the following is also true?

• A) p → q
• B) q → p
• C) p ∧ q
• D) ¬p ∨ ¬q

Q9: 9. What is the inverse of the statement "If it is snowing, then it is cold"?

• A) If it is not snowing, then it is not cold.
• B) If it is cold, then it is snowing.
• C) If it is not cold, then it is not snowing.
• D) If it is cold, then it is not snowing.

Q10: 10. If p → q is true, and q → r is false, then which of the following is true?

• A) p is false
• B) r is true
• C) q is true
• D) r is false

Q11: 11. Which of the following is equivalent to ¬(p ∨ q)?

• A) ¬p ∧ ¬q
• B) ¬p ∨ ¬q
• C) p ∧ q
• D) p ∨ q

Q12: 12. If p ∧ q is true, and q → r is true, then which of the following is true?

• A) r is true
• B) p is false
• C) q is false
• D) r is false

Q13: 13. What is the converse of the statement "If it is a weekday, then it is a workday"?

• A) If it is a workday, then it is a weekday.
• B) If it is not a workday, then it is not a weekday.
• C) If it is a weekend, then it is not a workday.
• D) If it is not a weekday, then it is not a workday.

Q14: 14. Which of the following is the contrapositive of the statement "If it is raining, then the grass is wet"?

• A) If the grass is not wet, then it is not raining.
• B) If the grass is wet, then it is raining.
• C) If it is not raining, then the grass is not wet.
• D) If the grass is wet, then it is not raining.

Q15: 15. If p ↔ q is true, and ¬p is true, then which of the following is true?

• A) q is false
• B) p is true
• C) q is true
• D) p is false

Q16: 16. What is the converse of the statement "If it is sunny, then it is warm"?

• A) If it is warm, then it is sunny.
• B) If it is not warm, then it is not sunny.
• C) If it is not sunny, then it is not warm.
• D) If it is warm, then it is not sunny.

Q17: 17. Which of the following is the negation of the statement "If it is Friday, then it is a movie night"?

• A) It is not Friday and it is not a movie night.
• B) It is Friday and it is not a movie night.
• C) It is not Friday or it is a movie night.
• D) It is Friday or it is not a movie night.

Q18: 18. If p ∧ q is false, and ¬p is true, then which of the following is true?

• A) q is true
• B) p is false
• C) q is false
• D) ¬q is true

Q19: 19. What is the contrapositive of the statement "If it is a party, then there is music"?

• A) If there is no music, then it is not a party.
• B) If there is music, then it is a party.
• C) If it is not a party, then there is no music.
• D) If there is music, then it is not a party.

Q20: 20. Which of the following is equivalent to ¬(p → q)?

• A) p ∧ ¬q
• B) p ∨ q
• C) ¬p ∧ q
• D) p ∧ q

Q21: 21. If p → q is true, and q ↔ r is true, then which of the following is true?

• A) r → p
• B) p ↔ r
• C) q → r
• D) p → r

Q22: 22. What is the contrapositive of the statement "If it is a weekday, then it is a school day"?

• A) If it is not a school day, then it is not a weekday.
• B) If it is a school day, then it is a weekday.
• C) If it is not a weekday, then it is not a school day.
• D) If it is a school day, then it is not a weekday.

Q23: 23. Which of the following is the negation of the statement "If it is sunny, then it is a good day"?

• A) It is not sunny and it is not a good day.
• B) It is sunny and it is not a good day.
• C) It is not sunny or it is a good day.
• D) It is sunny or it is not a good day.

Q24: 24. If p ↔ q is false, and ¬p is true, then which of the following is true?

• A) q is true
• B) p is false
• C) q is false
• D) p is true

Q25: 25. What is the converse of the statement "If it is cold, then it is winter"?

• A) If it is winter, then it is cold.
• B) If it is not winter, then it is not cold.
• C) If it is not cold, then it is not winter.
• D) If it is winter, then it is not cold.