Addition Rule of Implication - Assistance needed in understanding it.

[MathHelp]

Hi team,

So the addition rule of implication is as follows:

P therefore either P or Q.

Apparently, this is a logical implication because if you know P to be true then the overall statement "either P or Q" will always be true.

However, what if it was actually P and Q?

As an example:

I like cats (P). The addition rule of implication says that the following proposition must be true:

Either I like cats(P) or I like dogs(q).

But I actually like cats(P) and dogs (q). Doesn't that mean the rule can lead to errors?

 

[Genady]

By definition, logical OR is inclusive, i.e., either one of the parts is true regardless of the other. An exclusive OR, which does not allow for both parts to be true together, is usually written as XOR.