CmSc 180 Discrete mathematics
Homework 02: due 01/29
1. Problem 6. p. 14. Write the negations of the following statements:
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 is excellent
e. If the price is high then the food is good and the service is excellent
2. Problem 36, p.19. Four machines A, B, C, and D, are connected on a computer network. It is feared that a computer virus may have infected the network. Your security team makes the following statements:
a. If D is infected, then so is C.
b. If C is infected, then so is A.
c. If D is clean, then B is clean but C is infected
d. If A is infected, then either B is infected or C is clean
Assuming that these statements are all true, what can you conclude? Explain the reasoning process.
3. Problem 46, p. 33. Use propositional logic to prove that the following argument is a valid argument.
If my client is guilty, then the knife was in the drawer. Either the knife was not in the drawer, or Jason Pritchard saw the knife. If the knife was not there on October 10, it follows that Jason Pritchard did not see the knife. Furthermore, if the knife was there on October 10, then the knife was in the drawer and also the hammer was in the barn. But we all know that the hammer was not in the barn. Therefore, ladies and gentlemen of the jury, my client is innocent.
Note to problem 3: Here we do not question the truth of the statements in the argument. We assume that they are true. The question we have to answer is: is the argument a valid argument.
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