aconti said:1st proof: ¬P=>Q |- PvQ
2nd proof: P=>Q |- ¬PvQ
I think negation introduction and negation elimination should be used, can you share any thoughts on how you would work out the above?
Thanks
The purpose of proofing implications using negation is to determine the validity of a statement or argument. By using the negation of a statement, we can show that the original statement leads to a contradiction, thus proving it to be false.
To write a proof using negation, you start by assuming the opposite of the statement you want to prove. Then, you use logical steps and rules to reach a contradiction. This shows that the original statement is true.
P=>Q is the conditional statement "If P, then Q", while ¬P=>Q is the conditional statement "If not P, then Q". The main difference is the use of negation in the second statement, which can lead to different implications and conclusions.
Sure, let's say we want to prove the statement "If n is an even number, then n+1 is an odd number." We can do this by assuming that the opposite is true, that is, "If n is an even number, then n+1 is an even number." From there, we can use logical steps to show that this leads to a contradiction, thus proving our original statement to be true.
When proofing using negation, it is important to remember to start by assuming the opposite of the statement you want to prove, use logical steps and rules to reach a contradiction, and be clear and concise in your reasoning and conclusions.