Discrete Structures Test 1 from FALL 2002
Question 1. (8 points) Complete the following truth tables.
|A||B|| || || || |
|T||T|| || || || |
|T||F|| || || || |
|F||T|| || || || |
|F||F|| || || || |
Question 2. (10 points) Use a truth table to show that the following wff is a tautology.
Question 3. (12 points) Let A, B, C, and D be the following statements:
A: The villain is French.
B: The hero is American.
C: The heroine is British.
D: The movie is good.
a) Translate the following compound statements into propositional well-formed formulas (wffs).
b) Use A, B, C, and D as defined above to translate the following statements into English.
Question 5. (15 points) Using the statement letters E, Q, and B, translate the following English argument into propositional logic. (YOU DO NOT NEED TO PROVE THE ARGUMENT IS VALID!)
If the program is efficient, it executes quickly. Either the program is efficient, or it has a bug. However, the program does not execute quickly. Therefore, it has a bug.
Question 6. (10 points) Give an interpretation to prove that the following wff is not valid.
The domain of interpretation for x is
Question 7. (15 points) Prove the following wff using predicate logic.
Question 8. (10 points) Using the predicate symbols
H(x): x is can hit the baseball a long way
M(x): x can make a lot of money
T(x): x is a member of the Titans
k is the constant for Ken
translate the following verbal argument into a predicate logic wff.
Everyone who can hit a baseball a long way can make a lot of money. Ken is a member of the Titans. Ken can hit a baseball a long way. Therefore, some member of the Titans can make a lot of money.
(YOU DO NOT NEED TO PROVE THE ARGUMENT IS VALID!)