4.6 Disjunction introduction

The disjunction (that's the or) is very easy but not obvious:

$$\begin{fitch*} \par n & A \\ \par \hline \par & A \vee B & I$\vee$\ n \par \end{fitch*}$$

Well, to be exact, I will say that it's also available in the other order:

$$\begin{fitch*} \par n & A \\ \par \hline \par & B \vee A & I$\vee$\ n \par \end{fitch*}$$

That's wonderful, isn't it? If we know that ``it's Thursday'' we also know that ``it's Thursday or cows can fly'', ``it's Thursday or Friday'', or even ``it's Thursday... or not''. All of them are true.

But remember that, when talking, we tend to use exclusive or (XOR), which is true if one of the disjunctands is true but not when both of them are true at the same time. To a logician, the common phrase ``it's Thursday or Friday'' holds true under three situations: when it's Thursday, when it's Friday, and when it's Thursday and Friday at the same time (something difficult in the real world, but mathematicians are capable of doing all types of suppositions...).