Practice Exercises for Mathematical Logic 1. Začátek formuláře p q ~p p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q p https://www.mathgoodies.com/sites/default/files/lesson_images/or.gif q p https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif q T T _ T T T T F F _ T F F T T F _ T F F T F F _ Konec formuláře ___________________________________________________________________________________________________ 2. Začátek formuláře p q ~q p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q (p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q) https://www.mathgoodies.com/sites/default/files/lesson_images/conditional_transp.gif ~q _ T F T F T F _ F T F T F _ T F F T F _ Konec formuláře ___________________________________________________________________________________________________ 3. Začátek formuláře x y x https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif y y https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif x (x https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif y) https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif (y https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif x) x https://www.mathgoodies.com/sites/default/files/lesson_images/biconditional.gif y T T _ T T T T F F _ F F F T T F _ F F F T T T _ Konec formuláře 4. Which of the following statements from problem 3 is conditional? Začátek formuláře (_) x (_) y (_) x https://www.mathgoodies.com/sites/default/files/lesson_images/biconditional.gif y (_) None of the above. RESULTS BOX: _____________________________________________ Konec formuláře https://www.mathgoodies.com/sites/default/files/lesson_images/tab.gif 5. Which of the following statements from problem 3 is biconditional? Začátek formuláře (_) x https://www.mathgoodies.com/sites/default/files/lesson_images/conditional_transp.gif y (_) y https://www.mathgoodies.com/sites/default/files/lesson_images/conditional_transp.gif x (_) x https://www.mathgoodies.com/sites/default/files/lesson_images/biconditional_transp.gif y (_) None of the above. RESULTS BOX: _____________________________________________ Konec formuláře ___________________________________________________________________________________________________ 6. Začátek formuláře a b a https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif b (a https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif b) https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif a [(a https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif b) https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif a] https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif b T _ T T T T F _ F T F T T _ T F F T F _ Konec formuláře 7. Choose the word that best completes this sentence: The statement in the last column of the truth table in problem 6 is a ____________. Začátek formuláře (_) Biconditional (_) Tautology (_) Disjunction (_) None of the above. RESULTS BOX: _____________________________________________ Konec formuláře 8. Začátek formuláře p q ~q p https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif ~q p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q ~(p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q) (p https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif ~q) https://www.mathgoodies.com/sites/default/files/lesson_images/biconditional_transp.gif [~(p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q)] T T F _ T F T T F T T _ T T F T T T F _ T F F T T F T _ Konec formuláře 9. Which two statements from problem 8 are logically equivalent? Začátek formuláře (_) p https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif ~q and p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q (_) p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q and ~(p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q) (_) p https://www.mathgoodies.com/sites/default/files/lesson_images/conditional.gif ~q and ~(p https://www.mathgoodies.com/sites/default/files/lesson_images/and.gif q) (_) None of the above. RESULTS BOX: _____________________________________________ Konec formuláře https://www.mathgoodies.com/sites/default/files/lesson_images/tab.gif 10. Choose the word that best completes this sentence: The ____________ of two equivalent statements always yields a tautology. Začátek formuláře (_) Biconditional (_) Conjunction (_) Negation (_) All of the above. RESULTS BOX: _____________________________________________ Konec formuláře