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Exam-Style Question on LogicA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 204. This question is similar to one that appeared on an IB Studies paper in 2015. The use of a calculator is allowed.
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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