COT 3100 sec. #7094X
Quiz #1 - Propositional Logic
You have ten minutes. For this quiz, let E denote the following compound proposition:
E = (p /\ ¬q) 
(r 
p)
- Problem 1. (10 points):
- Fill in all of the empty columns of
the below truth table for E and its component sub-expressions.
Write T for true and F for false. (Partial credit will be given for
partially correct answers.)
| p
| q
| r
|
| ¬q
| p /\ ¬q
| r p
| E
|
|---|
| F | F | F | | | | |
|
| F | F | T | | | | |
|
| F | T | F | | | | |
|
| F | T | T | | | | |
|
| T | F | F | | | | |
|
| T | F | T | | | | |
|
| T | T | F | | | | |
|
| T | T | T | | | | |
|
- Problem 2. (10 points):
- Most of the following propositions can be easily seen to be
equivalent to E in just one or two steps using general
equivalence rules that you have learned. The other few propositions
are not equivalent to E at all. Mark the appropriate box to
indicate whether each proposition is equivalent to E. (Partial
credit will be given.)
| | Proposition | Equiv. | Not Equiv.
|
|---|
| a. | (p /\ ¬¬¬q) (r p) | |
|
| b. | ((r p)  (p /\ ¬q)) | |
|
| c. | (p /\ ¬q) (p r) | |
|
| d. | ¬((p /\ ¬q) (r p)) | |
|
| e. | (r p) (¬q /\ p) | |
|
| f. | (p /\ ¬q) (¬r \/ p) | |
|
| g. | (p /\ q) \/ (r /\ q) | |
|
| h. | (¬(¬p \/ q)) (r p) | |
|
| i. | (p /\ ¬q) \/ ¬(r p) | |
|
| j. | (p /\ ¬q) (¬p ¬r) | |
|