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Question id: 95. This question is similar to one that appeared in an IB Studies paper in 2011. The use of a calculator is allowed.

### Logic

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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