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5 marksLogic and Boolean Algebra

CAPE Applied Mathematics Unit 2 · 2008 (second paper) · Paper 2 · Question 2(e)

Use the laws of Boolean algebra to show that the Boolean expression (A ^ B) v (A ^ ~B) v (~A ^ ~B) is equivalent to A v ~B.

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Other parts of this question

  1. 2(a)Express in words: ~p ^ ~q.[3 marks]
  2. 2(b)Determine the truth value of the statement: 'London is in England or 2 x 3 = 5'.[3 marks]
  3. 2(c)By constructing the truth table for the proposition (p ^ q) => (p v q), determine whether this proposition is a tautology or a contradiction.[5 marks]
  4. 2(d)(i)Represent the Boolean expression (A ^ ~B) v [(~A v C) ^ B] as a switching circuit.[4 marks]
  5. 2(d)(ii)Represent ~a ^ (a v b) as a logic circuit using only AND, OR and NOT gates.[5 marks]

More practice: the rest of this paper · more Logic and Boolean Algebra questions · all CAPE Applied Mathematics Unit 2 past papers