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5 marksLogic and Boolean Algebra

CAPE Applied Mathematics Unit 2 · 2013 · Paper 2 · Question 1(e)(ii)

A switching circuit given by the Boolean expression p \wedge q \wedge (p \vee r) \wedge (q \vee (r \wedge p) \vee s).

Simplify this Boolean expression to obtain an equivalent expression and draw the corresponding circuit.

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Other parts of this question

  1. 1(a)Construct the truth table for (p \wedge q) \wedge \sim(p \vee q).[5 marks]
  2. 1(b)State, with reason, whether (p \wedge q) \wedge \sim(p \vee q) is a tautology or a contradiction.[2 marks]
  3. 1(c)Write a statement to show the proposition that is logically equivalent to \sim(p \vee q).[2 marks]
  4. 1(d)Using de Morgan's Law, or otherwise, write an equivalent statement to 'It is not true that it is hot and sunny.'[3 marks]
  5. 1(e)(i)Draw the circuit represented by this expression.[5 marks]
  6. 1(f)Use logic gates to represent the expression \sim[(p \wedge q) \vee r].[3 marks]

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