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Question id: 204. This question is similar to one that appeared in an IB Studies paper in 2015. The use of a calculator is allowed.

### Logic

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.

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