## 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 \(\lnot m \Rightarrow s\)

\(m\) | \(s\) | \(\lnot m\) | \(\lnot m \Rightarrow s\) |

T | T | ||

T | F | ||

F | T | ||

F | F |

(c) State whether \(\lnot m \Rightarrow s\) is a tautology, a contradiction or neither. Justify your answer.

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