Introduction to Logic
by
Stefan Waner and Steven R. Costenoble

Answers to Exercises
for
Section 4: Tautological Implications and Tautological Equivalences

3. The Conditional and the Biconditional 4. Tautological Implications and Tautological Equivalences 5. Rules of Inference Main Logic Page "Real World" Page
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11. p = "some cows are chickens;" q = "some chickens lay eggs." Then pq is true, whereas p is false. Thus, (pq)q is false.

13. p = "all swans are white;" q = "some swans are white." Then pq is true (since the statement p is false; not all swans are in fact white). On the other hand, qp says that, if some swans ar white, then all swans are white. But some swans are white, so that q is true; whereas p is false. Thus, qp is false. Therefore, (pq)(qp) is false.

15. Use the same example as in (13).

17. (ht)h Tautology

19. ~(rv)((~r)(~v)) Not a tautology

21. (ur)(~r~u) Tautology

23. (ur)(~r~u) Tautology

25. (gp)(g~p) Not a tautology

27. ((th)~t)h Tautology

29. ((gs)(gj))(sj) Not a tautology

31. ((gs)~g)~s Not a tautology

2. Logical Equivalence, Tautologies, ... 3. The Conditional and the Biconditional 4. Tautological Implications and Tautological Equivalences Main Logic Page "Real World" Page
Return to Exercises

We would welcome comments and suggestions for improving this resource. Mail us at:
Stefan Waner (matszw@hofstra.edu) Steven R. Costenoble (matsrc@hofstra.edu)
Last Updated: July, 1996
Copyright © 1996 StefanWaner and Steven R. Costenoble