Sentence | Symbolic Form |
---|---|

It is not cold. | ~r |

It is cold and sunny. | r ∧ s |

It is cold or sunny. | r ∨ s |

It is not cold but sunny. | ~r ∧ s |

It is neither cold nor sunny. | ~r ∧ ~s |

- p = "you get an A on the final exam"
- q = "you do every exercise in this textbook"
- r = "you get an A in this class"

Question: Write the following propositions using p, q, and r and logical connectives.

- To get an A in this class it is necessary for you to get an A on the final exam.
**Solution:**p → r - You do exery in this textbook; You get an A on the final exam, implies, you get an A in this class.
**Solution:**q ∧ p → r - Getting an A on the final exam and doing every evercise in this textbook is sufficient for getting an A in this class.
**Solution:**p ∧ q → r

- p = "you have the flu"
- q = "you miss the final exam"
- r = "you pass the course"

Question: Express the following propositions as an English sentence.

- p → q.
**Solution:**If you have flu, then you will miss the final exam. - ~q → r.
**Solution:**If you don't miss the final exam, you will pass the course. - ~p ∧ ~q → r.
**Solution:**If you neither have flu nor miss the final exam, then you will pass the course.

Date of last modification: February 27, 2019