Exam-Style Question on Logic
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 95. This question is similar to one that appeared on an IB Studies paper in 2011. The use of a calculator is allowed.
At Valley Park school, students must choose at least one of three after-school activities: Sport, Music or Adventure.
Consider the following propositions about one of the students called Raj:
\(s\): Raj chooses Sport,
\(m\): Raj chooses Music,
\(a\): Raj chooses Adventure.
(a) Write, in words, the compound proposition$$\lnot s \Rightarrow (m \lor a)$$
(b) Complete the truth table for \(\lnot m \Rightarrow s\)
|\(m\)||\(s\)||\(\lnot m\)||\(\lnot m \Rightarrow s\)|
(c) State whether \(\lnot m \Rightarrow s\) is a tautology, a contradiction or neither. Justify your answer.
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