SOLUTION: I am actually getting myself confused here: Please Help!
a.) If today is Monday, then tomorrow is not Wednesday.
b.) If it is false that today is Monday and tomorrow is not W
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Question 185765This question is from textbook A Survey of Mathematics with Application
: I am actually getting myself confused here: Please Help!
a.) If today is Monday, then tomorrow is not Wednesday.
b.) If it is false that today is Monday and tomorrow is not Wednesday
c.) Today is not Monday or tomorrow is Wednesday.
I personally would say that A & B are equivalent, but the more I read over it and convince myself that A & B are equivalent, the more I confuse myself. Can you please help me determine which statements are equivalent. Thanks A million everyone
This question is from textbook A Survey of Mathematics with Application
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let P = today is Monday and Q = today is Wednesday
Now translate:
a) "If today is Monday, then tomorrow is not Wednesday" translates to "If P then Q" which symbolically looks like 
Now fill out a truth table:
| P | Q |  | |
| T | T | F | F |
| T | F | T | T |
| F | T | F | T |
| F | F | T | T |
Note: let me know if you need help constructing a truth table
The truth values in red are the values we're going to compare later.
b) "If it is false that today is Monday and tomorrow is not Wednesday" translates to "It is NOT the case that P and not Q are true".
In symbolic form, the expression looks like: )
Now fill out a truth table:
| P | Q | |  |
|
| T | T | F | F | T |
| T | F | T | T | F |
| F | T | F | F | T |
| F | F | T | F | T |
c)
"Today is not Monday or tomorrow is Wednesday" translates to "Not P or Q" which looks like 
Now make a truth table
| P | Q |  | |
| T | T | F | T |
| T | F | F | F |
| F | T | T | T |
| F | F | T | T |
--------------------------------------------------------------------
Now comparing the truth values that are marked in red from parts a) to c), we see that the red truth values in tables b) and c) are identical. So this means that statements b) and c) are equivalent.
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