Reasoning and Logic · CAPE Pure Mathematics Unit 1

33 past-paper questions on Reasoning and Logic, part of Basic Algebra and Functions, from every CAPE Pure Mathematics Unit 1 paper on Quelpr.

1. Q21 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (Rest of Region) · Paper 1Which of the following statements is true?
2. Q31 mark · multiple choice· CAPE Pure Mathematics Unit 1 · 2008 (T&T) · Paper 1Which of the following statements is true?
3. 1(a)(i)3 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2Let p and q be any two propositions. Complete the truth table below.
4. 1(a)(ii)2 marks· CAPE Pure Mathematics Unit 1 · 2022 · Paper 2Hence, state whether the statements (\sim q \wedge p) and p \vee (\sim q \wedge p) are logically equivalent. Justify your response.
5. Q141 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2010 · Paper 1Which of the following statements is FALSE?
6. Q31 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2012 · Paper 1Which of the following statements is true?
7. Q141 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1The statement p \lor \sim p is a
8. Q151 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2013 · Paper 1The statement \sim(p \lor (\sim p \land q)) is logically equivalent to
9. Q31 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2014 · Paper 1The inverse of p \rightarrow q is
10. Q101 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1The statement \sim(p \vee (\sim p \wedge q)) is logically equivalent to
11. Q111 mark · multiple choice· CAPE Pure Mathematics Unit 1 · May/June 2015 · Paper 1Which of the following statements is true?
12. 1(a)(i)3 marks· CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2Complete the truth table for p \to q, q \to p, and (p \to q) \wedge (q \to p).
13. 1(a)(ii)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2Hence, state whether the statements q \to p and (p \to q) \wedge (q \to p) are logically equivalent. Justify your response.
14. 1(a)(i)4 marks· CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2Complete the truth table for p, q, r, p ⇒ q, q ⇒ r, (p ⇒ q) ∧ (q ⇒ r), p ∨ q, and (p ∨ q) ⇒ r.
15. 1(a)(ii)2 marks· CAPE Pure Mathematics Unit 1 · May/June 2026 · Paper 2Determine whether (p ⇒ q) ∧ (q ⇒ r) is logically equivalent to (p ∨ q) ⇒ r. Justify your response.
16. 1(a)1 mark· Pure Mathematics · Unit 1 Q1 1(a)Construct a truth table for the statements
17. 1(a)5 marks· Pure Mathematics · Unit 1 Q1 1(a)Construct a truth table for the statement (p → q) ∧ (r → q).
18. 1(a)(i)4 marks· Pure Mathematics · Unit 1 Q1 1(a)(i)Let p and q be any two propositions. Complete the truth table below.
19. 1(a)(i)5 marks· Pure Mathematics · Unit 1 Q1 1(a)(i)Copy and complete the truth table below for the propositions (p ^ q) → r and (p → r) ^ (q → r).
20. 1(a)(i)1 mark· Pure Mathematics · Unit 1 Q1 1(a)(i)Write EACH of the statements below in terms of p and q. It is not raining or John is sick.
21. 1(a)(i)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(i)State the inverse and the contrapositive of the statement p → q.
22. 1(a)(i)4 marks· Pure Mathematics · Unit 1 Q1 1(a)(i)Complete the truth table below.
23. 1(a)(i)1 mark· Pure Mathematics · Unit 1 Q1 1(a)(i)p → q
24. 1(a)(ii)4 marks· Pure Mathematics · Unit 1 Q1 1(a)(ii)Copy and complete the table below to show the truth table for p → q and ~q → ~p.
25. 1(a)(ii)1 mark· Pure Mathematics · Unit 1 Q1 1(a)(ii)Hence, state whether the statements ~(p ∨ q) and ~p ∧ ~q are logically equivalent. Justify your response.
26. 1(a)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(ii)Hence, determine whether or not (p ^ q) → r and (p → r) ^ (q → r) are logically equivalent. Justify your response.
27. 1(a)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(ii)Hence, state whether the statements ~(p ∨ q) and ~p ∧ ~q are logically equivalent. Justify your response.
28. 1(a)(ii)1 mark· Pure Mathematics · Unit 1 Q1 1(a)(ii)Write EACH of the statements below in terms of p and q. If it is raining then John is not sick.
29. 1(a)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(ii)~(p ∧ q).
30. 1(a)(iii)2 marks· Pure Mathematics · Unit 1 Q1 1(a)(iii)Hence, state whether the compound statements p ↔ q and ~q → ~p are logically equivalent. Justify your response.
31. 1(b)(i)1 mark· Pure Mathematics · Unit 1 Q1 1(b)(i)Write the converse of the statement "n is an integer ⇒ n² is an integer".
32. 1(c)(i)4 marks· Pure Mathematics · Unit 1 Q1 1(c)(i)Complete the truth table below:
33. 1(c)(ii)2 marks· Pure Mathematics · Unit 1 Q1 1(c)(ii)State, giving a reason for your response, whether the following statements are logically equivalent: p → q and ¬(p ∨ q) → (p ∧ q).