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3 marksThe Real Number System – ℝ

CAPE Pure Mathematics Unit 1 · May/June 2018 · Paper 2 · Question 1(b)(ii)

A binary operation ⊗ is defined on the set of real numbers, R, as a ⊗ b = 2a + 3b for all a, b in R.

Prove that ⊗ is closed in R.

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Other parts of this question

  1. 1(a)(i)Let p and q be any two propositions. Complete the truth table below.[4 marks]
  2. 1(a)(ii)Hence, state whether the statements ~(p ∨ q) and ~p ∧ ~q are logically equivalent. Justify your response.[1 mark]
  3. 1(b)(i)Calculate 5 ⊗ 2.[1 mark]
  4. 1(b)(iii)Determine whether ⊗ is commutative.[3 marks]
  5. 1(c)Calculate the values of a, b and c.[7 marks]
  6. 1(d)Solve the logarithmic equation log₄(2x + 2) - log₄(x + 1) = 1.[6 marks]

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