# Help on logic

1. Jan 19, 2012

### Mnyx

Hello all

I don't write much, I mainly follow you silently. Great forum
I have a doubt that to many of you will seem absolutely silly but it has been bugging me for days.

I am trying to find the correct interpretation to a non-english administrative act and trying to use all possible angles

The question is

How do I interpret this paragraph using boolean algebra?

PARAGRAPH:

It shall be deemed a “new car”, a vehicle that:

Has never been out of the factory

Or

Has never been registered with motorization

Or

Doesn’t have any scratches

END OF PARAGRAPH

Would you interpret that all three conditions need to be satisfied for the vehicle to be a “new car” because they are negative statements or that only one of the three conditions needs to be met?

I was wondering if you guys could give me your thoughts on this?
thanks

2. Jan 19, 2012

### Nile3

Hello, here's my take on this:

Let

of : Has been out of the factory
m : Has been registered with motorization
s : has scratches

then

!of v !m v !s

Where v is or and ! is not.

Only one of these conditions has to be met to satisfy that it is a true statement.

Truth table, look at the before last column to get the result

F | M | S | !F v !M *v* !S
---+---+---+--------------
0) T | T | T | F F F *F* F
1) T | T | F | F F F *T* T
2) T | F | T | F T T *T* F
3) T | F | F | F T T *T* T
4) F | T | T | T T F *T* F
5) F | T | F | T T F *T* T
6) F | F | T | T T T *T* F
7) F | F | F | T T T *T* T

Therefore if F,M or S is true, it's not a new car.

3. Jan 19, 2012

### SW VandeCarr

In Boolean arithmetic: 1+1=1, 1+0=1, 0+1=1, 0+0=0.

Although the statements are negative, the proper interpretation IMO is that if the statement is affirmed it should be assigned the Boolean value of 1, and 0 if it is not affirmed.

So "It is true that the car has no scratches, therefore the car is new". (Idiotic, but logically follows from the premise). If this were the only affirmed statement, we have 0+0+1=1, where the conclusion "The car is new" is affirmed.

Last edited: Jan 19, 2012
4. Jan 20, 2012

### Mnyx

I can't thank you enough for helping me think this through

I am still trying to figure this out

Just to explain a bit better. Some of the statements seem idiotic because I oversimplified the wording and changed the subject matter a bit.
However, I was faithful to the spirit of the administrative act I am trying to decipher, where "new" is defined in relation to three negative statements that go from a first one that is almost impossible to meet to a third one that is satisfied by an abnormally large number of cases (and on its own represents a very odd definition of "new")

5. Jan 20, 2012

### SW VandeCarr

Your welcome. I thought this was just an example and you were interested in using Boolean logic to reach a conclusion. Your confusion seems to be in thinking that so called "negative" statements must somehow be false. They are just propositions which can be true or false. "I am not the King of Spain" is a proposition. It is true. There is no necessity to convert the statement to "I am the King of Spain" and declare it false. They both mean exactly the same thing. The key point here in terms of logic is the interpretation of the OR connective.