I’ll illustrate how this works in logic-ex. Let’s say we want to construct the truth table for A or not A.

The first thing I need is more rows, so I hit the circled plus thing.

Now I’ve got a second row, and in this case two rows is enough. Time to start filling in values ...

I’m doing the reference columns first because these are always the same and I don’t need to work out what the values are.

Now I have to enter the value of A or not A when A is true. You might be able to compute this in value in your head, but that won’t always be the case. I expect that, often, before you enter a value in the table in zoxiy you will have taken a pencil and paper and worked out the truth table step by step.

So what you enter will often be something that took quite a bit of work to compute.

Or you could just guess. But this is not generally a good strategy because I take the view that a truth table is either right or wrong, and if you are really guessing you only have a 1/16 chance of being right for most truth tables.

Anyway, I think it’s true.

Now for the last truth value.

This is also true.

We’re not done yet, we now have to say whether the sentence is a contradiction. A \emph{contradiction} is a sentence that is false in all possible situations.

This sentence isn’t false in all possible situations ...

... so it isn’t a contradiction.

Next we have to specify whether ‘A or not A’ is a logical truth. A \emph{logical truth} is a sentence that is true in all possible situations.

This sentence is true in all possible situations ...

... so this sentence is a logical truth.

Finally, we’re asked whether the sentence is a logical possibility. A \emph{logical possibility} is a sentence that is true in one or more possible situations.

This sentence is true in at least one possible situation ...

... so this sentence is a logical possibility.