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4 marksLogic and Boolean Algebra

CAPE Applied Mathematics Unit 2 · 2011 · Paper 2 · Question 1(d)(ii)

Propositions p and q are given by: p: There is a west wind. q: We shall have rain.

Construct a truth table to prove that the statements in parts (d)(i)a) and (d)(i)b) are equivalent.

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Other parts of this question

  1. 1(a)Construct a truth table to show that the proposition (~ p ˅ ~ q) ⇒ (p ˄ ~ q) ALWAYS takes the value of p.[5 marks]
  2. 1(b)Write the Boolean expression for the given logic circuit.[4 marks]
  3. 1(c)Draw a switching circuit to represent the expression (a ˄ b) ˅ [a ˄ (~ b ˅ c)].[4 marks]
  4. 1(d)(i)a)Express the statement 'If there is a west wind then we shall have rain' in logic form using the connectives ~ and ⇒.[2 marks]
  5. 1(d)(i)b)Express the statement 'If there is no rain then the west wind does not blow' in logic form using the connectives ~ and ⇒.[2 marks]
  6. 1(e)Use de Morgan's laws to prove that ~ [(p ˄ q) ˅ ~ p] = ~ q ˄ p.[4 marks]

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