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I have seen both of these symbols used for equivalence.
You wrote:Well....according to my lecture....it's not a tautology...
I wrote:It looks to me like it isn't, so you need to find an example.
Ok. So we agree. My problem is, I'm not sure what sort of example is required. Here's a possibility:
A ={he plays football} B = {he plays hockey} C = {he plays tennis}
Now consider the case where he does not play football, does play hockey and does not play tennis.
B => C is False but A => (B => C) is True. (True => False) is False but (False => False) is True.
A => B is True and (A => B) => C is False. (False => True) is True but (True => False) is False.
Thus the two statements give different results in this case.
[note: I identified this case by looking at my truth table. I do not know how I can 'prove' my argument without using the words true and false.]
Bob
Well.....I try this before....my lecture say I should used formula(logical algebra) to prove it but not example of TRUE or false value..
Now trying to get some tips and example from him....hope they can provide me..
What does the equivalent symbol mean?
you mean this "≡" ?
In my book it's called "Boiconditional Proposition" or " A if and only if B"...
hi envy1987
Although they want you to avoid the truth table, I see no harm in separately trying it, just to see if it is a tautology. (You don't have to submit that as part of your answer.) It looks to me like it isn't, so you need to find an example. Have you been given any examples for other non tautologies so I can get an idea what is expected here?
Bob
Nope....what I post here is the overall of the question.....
Well....according to my lecture....it's not a tautology...
I do facing a problem when I solving one of my homework.
The question as below.
Q: If the statement is a tautology, give a proof using the appropriate rules of logic and avoid using truth tables if possible.If it is not a tautology, then justify your answer by giving an appropriate example.
( A→(B→C)) ≡ ((A→B)→C)
Below is my answer
¬A∨(B→C) ≡ ((¬A∨B)→C)
¬A∨(¬B∨C) ≡ ¬(¬A∨B)∨C
(¬A∨¬B)∨C ≡ ¬(¬A∨B)∨C
Then I stuck at here.....please give me some advice pls...
Thank a lot for your fast reply ^.^
Hi ,
I just having my DISCRETE MATHEMATICS course for this semester and I do facing on solving below question.
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F and G is a positive integer
f : N →R
g : N →R
Find the composition f ° g and g ° f.
f(n) = e^n ,
g(n) = e^(e^n )
=================================================================
Did the answer below fulfill the question need?
g(f(n)) = e^(e^(e^n))
f(g(n)) = e^(e^(e^n))
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