"Do you want pancakes or waffles?"

"Yes."

I wanted to start this blog saying that everyone has had a similar conversation, but I don't know if that is true. However, what is important, is the meaning of the question. Most people would understand the question above as "choose either pancakes or waffles". The expected answer is usually one of "pancakes" and "waffles". However, as someone who dabbles in programming languages and logico-linguistics, the definition of this word is different.

In both of those topics, the word "or" is used to refer to whether either of the statements are fulfilled. In other words, a phrase with "A or B" is usually evaluated as a Boolean value. Does that make the whole thing more confusing? Probably, but let me explain. A Boolean value is either true or false with nothing in between. When we evaluate something in these 2 contexts, we only consider the truth value of the statement.

For instance, the question "are you feeling hot or cold?" can be considered this way: If the person is hot, the truth value of the statement is true. If the person is cold, the truth value is also true. The truth value of the question is false only if the person is neither hot nor cold (e.g. warm).

Another example would be "are you going to the library or the bookstore?". If you're going to the library, you can answer "Yes". If you're going to the bookstore, you can also answer "Yes". That is because either of those destinations makes the phrase's truth value true.

That leads me to something called "exclusive or", or as programmers call it, "XOR", or as it is denoted in Mathematics, "⊕". In the statement "A XOR B", only one of A and B can be true. If A and B are both true, "A XOR B" has the truth value of false. This means if you answer both pancakes and waffles to the question at the start of the blog, the answer would be "no".

I've noticed that in daily language, the word "or" is used more in the "XOR" context. You may get asked "would you like that with spaghetti or fries?" in a restaurant, or "cash or card" when paying a bill. Questions expect you to choose one of the options, essentially meaning the word "either" without using it.

Anyhow, here's my (perhaps incoherent) observation on this common word that we use very often. Did you find this interesting or uninteresting? Your answer can simply be "yes".