## Exam-Style Questions on Logic## Problems on Logic adapted from questions set in previous 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 \(f\Rightarrow e\).

(c) Determine whether your statement in part (a) is logically equivalent to your statement in part (b). Justify your answer.

## 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.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

To search the **entire Transum website** use the search box in the grey area below.

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Kausar Begum Khan, Kenya

Friday, January 26, 2018

"This is a fabulous website! I cannot thank you enough."

Aruna Upadhyayula, Bahrain

Tuesday, November 6, 2018

"Transum is so resourceful. The resources are so child-friendly that my students love its usage.It has a wide range of topics and caters to most of my needs. 'Thankyou" will be too small a word to express my gratitude to the content developers of this site."

Ahmed Jaja, Ghana

Thursday, November 22, 2018

"It was very useful for me.I recommend it to every math student.Thank you."