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3 marksReasoning and Logic

CAPE Pure Mathematics Unit 1 · May/June 2023 · Paper 2 · Question 1(a)(i)

Two propositions p and q are given.

Complete the truth table for p \to q, q \to p, and (p \to q) \wedge (q \to p).

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Other parts of this question

  1. 1(a)(ii)Hence, state whether the statements q \to p and (p \to q) \wedge (q \to p) are logically equivalent. Justify your response.[2 marks]
  2. 1(b)Let x and y be negative real numbers and let z be any real number. Use a counter example to show that the statement "if x > y then xz > yz" is false.[3 marks]
  3. 1(c)The expression f(x) = 6x^3 + px^2 + qx + 2 is divisible by 2x - 1 and has a remainder of 2 when divided by x - 1. Calculate the values of p and q.[9 marks]
  4. 1(d)(i)Solve the logarithmic equation \log_3(x^2 - 9) - \log_3(x + 3) = 3.[4 marks]
  5. 1(d)(ii)Show that \sqrt{320x^3} + \sqrt{125x^3} simplifies to 13x\sqrt{5x}.[4 marks]

More practice: the rest of this paper · more Reasoning and Logic questions · all CAPE Pure Mathematics Unit 1 past papers