# Challenge Exercises for Mathematical Logic

**Directions**: Read each question below. Create a truth table to help you answer each question. The answer choices provided correspond to the last column of the truth table for a given problem. Select your answer by clicking on its button. Feedback to your answer is provided in the RESULTS BOX. If you make a mistake, choose a different button.

1. |
What are the truth values for this statement? ~pq |

2. |
What are the truth values for this statement? p~q |

3. |
What are the truth values for this statement? ~ab |

4. |
What are the truth values for this statement? a~b |

5. |
Choose the word or phrase that best completes this sentence: The statements in problems 3 and 4 are ____________. |

6. |
What are the truth values for this statement? ~qp |

7. |
Which statement below is logically equivalent to the statement in problem 6? |

8. |
What are the truth values for this statement? ~r~(rs) |

9. |
What are the truth values for this statement? (~qp)(pq) |

10. |
Choose the word or phrase that best completes this sentence: The statements given in problems 8 and 9 are _______. |