By Judith L. Gersting
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Additional info for Mathematical Structures for Computer Science: A Modern Treatment of Discrete Mathematics
A-(B -A) g. AAB<- B' VA' h. (AVB')A(AAB)' i. [(AvB)AC'] -A'vC *15. A memory chip from a microcomputer has 24 bistable (ON-OFF) memory elements. What is the total number of ON-OFF configurations? 16. Verify the equivalences in the list on page 8 by constructing truth tables. ) 17, Verify by constructing truth tables that the following wffs are tautologies. *a. AVA' e. (AVB)' - A'AB' (De Morgan's law) b. (A')' - A f. (A A B)' <-A' V B' (De Morgan's law) *c. AAB -B g. AVA*-,A d. A-eAvB 18. Prove the following tautologies by starting with the left side and finding a series of equivalent wffs that will convert the left side into the right side.
2Ž7or3iseven. 6. Write the negation of each statement. *a. If the food is good, then the service is excellent. *b. Either the food is good or the service is excellent. c. Either the food is good and the service is excellent, or else the price is high. d. Neither the food is good nor the service excellent. e. If the price is high, then the food is good and the service is excellent. Section l. Statements, Symbolic Representation, and Tautologies 15 7. Write the negation of each statement. a. The processor is fast but the printer is slow.
2 Review TECHNIQUES * Apply derivation rules for propositional logic. * Use propositional logic to prove the validity of a verbal argument. MAIN IDEAS * A valid argument can be represented by a wff of the form Pi A P2 A P3 A A Pn - Q that is a tautology. * A proof sequence in a formal logic system is a sequence of wffs that are either hypotheses or derived from earlier wffs in the sequence by the derivation rules of the system. 30 FormalLogic * The propositional logic system is complete and correct; valid arguments and only valid arguments are provable.