Homework 2

Reminder: Late homeworks will NOT be accepted!

1. Rosen, Section 1.2, 7a,c,e
2. For each implication in Question 1, show the implication is a tautology without using truth tables. This is done by using a series of logical equivalences to show the implication is logically equivalent to T. Format your proof as in class, giving the rule(s) from Tables 5 and 6 that apply.
3. A logician told her child, ``If you don't finish your dinner, you will not get to stay up and watch TV.'' The child finished dinner and then was sent straight to bed. Discuss.
4. Rosen, Section 1.2, 15. (Note that this means that implication is not associative.)
5. Rosen, Section 1.2, 16. Use a series of logical equivalences for this proof, not a truth table. Use the format described above.
6. Rosen, Section 1.2, 17. Again, use a series of logical equivalences for this proof. You may use the additional logical equivalence that is not in Tables 5 and 6:

   

7. Rosen, Section 1.2, 25.
8. Rosen, Section 1.3, 10
9. Rosen, Section 1.3, 20
10. Rosen, Section 1.3, 30

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