## Exam-Style Question on Logic## A 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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