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

Algebra ->  Conjunction -> 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      Log On


   

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) About Me  (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:

PQ
TTFF
TFTT
FTFT
FFTT



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:

PQ
TTFFT
TFTTF
FTFFT
FFTFT



c)
"Today is not Monday or tomorrow is Wednesday" translates to "Not P or Q" which looks like

Now make a truth table
PQ
TTFT
TFFF
FTTT
FFTT

--------------------------------------------------------------------



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.