OCR MEI D2 2007 June — Question 1

Exam BoardOCR MEI
ModuleD2 (Decision Mathematics 2)
Year2007
SessionJune
TopicTrig Proofs

1
  1. A joke has it that army recruits used to be instructed: "If it moves, salute it. If it doesn't move, paint it." Assume that this instruction has been carried out completely in the local universe, so that everything that doesn't move has been painted.
    1. A recruit encounters something which is not painted. What should he do, and why?
    2. A recruit encounters something which is painted. Do we know what he or she should do? Justify your answer.
  2. Use a truth table to prove \(( ( ( m \Rightarrow s ) \wedge ( \sim m \Rightarrow p ) ) \wedge \sim p ) \Rightarrow s\).
  3. You are given the following two rules. $$\begin{aligned} & 1 \quad ( a \Rightarrow b ) \Leftrightarrow ( \sim b \Rightarrow \sim a )
    & 2 \quad ( x \wedge ( x \Rightarrow y ) ) \Rightarrow y \end{aligned}$$ Use Boolean algebra to prove that \(( ( ( m \Rightarrow s ) \wedge ( \sim m \Rightarrow p ) ) \wedge \sim p ) \Rightarrow s\).