
Formal Proof
Hello, sorry if this is in the wrong place, i wasn't really sure which one it is.
Anywho,
I'm struggling a bit with my Logic & Sets module and would appreciate a bit of help.
The first thing that is confusing me is the term formal proof. I'm just not sure what exactly it means, my maths text book says there are lots of different ways to use formal proof, but then doesn't bother to tell you them.
For example, a question i have to answer is:
Explain how to use a formal proof to show that a set of statements is inconsistent.
Now i'm not here looking for someone to give me the answers, as i would like to get to grips with this myself and understand it, so if i post what i wrote for this question, could you tell me if i'm anywhere near being right? And if not, point me towards the correct direction. Thanks.
This is what i wrote for that question [Which reading it back sounds like a load of gibberish to be honest :/ ]:
"
To show that a set of statements is inconsistent using formal proof, I would attempt to provide a
Counterexample by assuming it to be true and therefore proving it to be false..
Eg:
Specification:
If the operator presses the alarm and the core temperature is not rising rapidly, then the control
process does not shut down the reactor.
Proposition:
The operator presses the alarm and the core temperature is not rising rapidly, and the control
process does close down the reactor.
A = The Operator presses the alarm, C = The core temperature is not rising rapidly, P = The control
process closes down the reactor.
(A ^ C) => ¬P
Assuming then that A, C & P are all true that makes it:
True ^ true => ¬true
True => ¬true
True => false
And if true implies false then the truth value of the statement is false, therefore inconsistent."
I do have some other questions as well, but i'll leave them for now until i understand this one.
Thank you.