(If someone knows the codes for the correct symbols, could you please PM them to me.)

Interesting title, no?

Let me explain this. The first symbol, which I have typed as a 3 should in fact be that backwards E. The second symbol, the -/ should be an upside down A. Now that that is clear, I will only use E and A for the rest of this.

There are two types of claims someone can make. The first is the E claim, which goes along the lines of "There exist (statement A) such that (statement B)".

The second type is "For all (statement A) (statement B)"

Now, to disprove these two (the most common thing done around here with statements), one needs to prove the inverse.

Lets look at an example.

E pizza such that pizza has cheese on it.

Let just say, for whatever reason, we wanted to disprove that. To do that we would have to prove this:

A pizza there is no cheese on it.

Now, if we think about it, we disprove there being any pizza with cheese on it by saying that all pizza does not have cheese.

The opposite way to disprove is this.

A pizza, there is cheese on it.

To disprove this, we would have to say:

E pizza with no cheese on it.

So, the end result is this.

To disprove:
A (item) (claim about item)
we have to prove:
E (item) !(claim about item)

To disprove:
E (item) (claim about item)
we have to prove:
A (item) !(claim about item)

The ! means the opposite. As in the example, the claim was has cheese, the opposite is doesn't have cheese. Having anchovies is not the opposite of having cheese, only not having cheese is.


The reason I am posting this is that recently I saw some examples of people trying to disprove some statement which includes qualifiers, there by making it a "E" statement (or is it an "E" statement?) by showing themselves (or another "E" statement), since they were opposite the original statement, as sufficient disproof of the original statement, when in fact that is false.