 # Exam-Style Questions on Logic

## Problems on Logic adapted from questions set in previous Mathematics exams.

### 1.

IB Studies

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.

### 2.

IB Studies

Two propositions $$e$$ and $$f$$ are defined as follows

$$e$$: Nigel is exercising regularly,

$$f$$: Nigel is getting fitter.

(a) Write down the following statement in words.

$$f\Rightarrow e$$

(b) Write down, in words, the contrapositive statement of $$f\Rightarrow e$$.

### 3.

IB Studies

Consider the following statements.

$$p$$: the actor was cast for a part in a play
$$q$$: the actor has learned all of her lines
$$r$$: the actor is ready for the dress rehearsal

(a) Write the following argument in symbolic form.

"If the actor was cast for a part in a play and has learned all of her lines, then the actor is ready for the dress rehearsal."

(b) Complete a truth table for the argument in part (a). Begin your truth table as follows.

 $$p$$ $$q$$ $$r$$ T T T T T F T F T T F F F T T F T F F F T F F F

(c) Use your truth table to determine whether the argument in part (a) is valid. Give a reason for your decision.

Write down the inverse of the argument in part (a)

(d) in symbolic form;

(e) in words.

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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