Truth Tables

Hi,

Sorry if this thread doesn't belong here... but anyways I need help understanding a truth table I was given. I think I understand it for the most part but I'm confused as to how the last statement results in a true value?

p = T
q = F
p Λ q = F
p V q = T
~ ( p Λ q) = T
(p Λ q) V ~ (p V q) = T


I worked out the last statement as follows:

(p Λ q) = F
(p V q) = T
~(p V q) = F
(F) V F = F

So that contradicts what the book says. Also I checked the errata for this book too and it doesn't mention this as an error. So I'm guessing I got something wrong with precedence.. any help would be greatly appreciated. Thank you!

EDIT: I pulled the statement from this truth table:
http://img258.imageshack.us/img258/9333/ttableme4.jpg

IF that is all the information you are given, then the solution is indeterminate.

For example "If P is True then Q is True" does not impose ANY contraints on Q if P is False.

It is the same below:

T^F is known to be F by virtuel of the first three statements. But
T^T F^T F^F are ALL unknown results.....

Hi CPUWizard, thanks for taking the time to help me out.

I'm a bit confused now how the solution is indeterminate.. are you suggesting that p and q actually have different values in the last statement than the other statements? If so, wouldn't that contradict the table? I should have stated this before but the values I gave in my post were from a specific row in the following table:


p | q | p Λ q | p V q | ~ ( p Λ q) | (p Λ q) V ~ (p V q)

T T T T F T
T F F T T T
F T F T T T
F F F F T T

EDIT: Sorry about the poor quality of the table, it's difficult to format with this editor. I'll try to post an image.

EDIT 2: I uploaded an image of the table. Here it is:
http://img258.imageshack.us/img258/9333/ttableme4.jpg

It does look like the last column heading should be (p V q ) V ~ ( p Λ q) instead of (p Λ q) V ~ (p V q)

What I am stating is that you have NOT provided sufficient EXPLICIT information. There is NO definition of "v" and "^". Thereofre....

1) Only one (out of a possible 4) input patterns yields a defined output

or

2) You are using the conventional meanings (which makes parts 3&4 redundant).

Would you expect an arithmetic question to start with a definition + and - ? It is sparingly unlikely that any text book on logic which uses standard logical and and or symbols to mean anything else, but unfortunately common for basic typos to exist in them. I've even got one where no 'fi' ligatures are printed, which makes it completely unreadable.

My apologies.. I thought those symbols were universal in meaning. Here are their definitions:

~ stands for 'not'
Λ stands for 'and'
V stands for 'or'


I'm going to assume that what pm_kirkham said is the case.. I can't see any way that the entire last column consists of just true values without contradicting prior statements.

Thanks for your guys' help btw

The Λ and V are indeed very standard (although they are usually represented by U and not V, I understood their meaning).

I think you are reading too much into the problem.

(p Λ q) V ~ (p V q) = T

Is a false statement, plain and simple. It is probably just a typo or some oversight.

(p Λ q) = F
(p V q) = T
-------------
~(p V q) = F

Therefore: F V F != T

EVEN if they are saying that V is an exclusive or.

How to code truth table in program ?

Quote:

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Originally Posted by ProgramThis

The Λ and V are indeed very standard (although they are usually represented by U and not V, I understood their meaning).

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I agree that they are, but then the post contains redundant information:

Quote:

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(p Λ q) = F
(p V q) = T

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Since the source of the 'problem' was unknown, makin any assumptions would [IMHO] be a mistake.

Quote:

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Originally Posted by Peter_APIIT

How to code truth table in program ?

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Do you want to code an equivalent sequence of conditional lines, or want a function which returns the right boolean answer, equal to an arbitrary truth table?
(Second option is easy)