Question 179192This question is from textbook
: Determine which, if any, of the three statements are equivalent.
a) If today is Monday, then tomorrow is not Wednesday
b) It is false that today is Monday and tomorrow is not Wednesday
c) Today is not Monday or tomorrow is Wednesday
I do not think any of these are equivalent, ?? Is this sound thinking...?
This question is from textbook
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! 11. (4 pts) Determine which, if any, of the three statements are equivalent.
a) If today is Monday, then tomorrow is not Wednesday
b) It is false that today is Monday and tomorrow is not Wednesday
c) Today is not Monday or tomorrow is Wednesday
p=today is monday
q= tomorrow is wednesday
a) p -> ~q
b) ~(p ^ ~q)
c) ~p v q
p q a) b) c)
t t f t t
t f t f f
f t t t t
f f t t t
statements b and c are equivalent
:
In Demorgan's Law, you can think of it almost like the distributive property. with a few tweeks
:so in b) to get rid of the parenthesis you would change the p to ~p and the ~q to q and instead of ^(and) it changes to v(or) so it becomes ~p v q . as you can see it is the same as c) so remember the signs change much like the + and - in distribution and the and "^" sign or the or "v" signs change from one to the other(inside and outside of the parenthesis)
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