Really nice explanation, Danny. I just wanted to tag on a thought about the symbol we use for conditional logic: The Arrow.
The arrow really is an outstanding symbol to use, because it implies direction. We start on the left side of the arrow, then we move to the right side of the arrow *if* (and only if) the triggering condition is met. If the condition on the left side of the arrow is NOT met, then the right side doesn’t matter – The whole rule doesn’t apply.
So let’s look at the rule: NOT J —> S
Now let’s look at the situation that has you confused: Both birds are in the forest. We start on the left side of the arrow, which says “NOT J.” Does that apply to this situation? No – Jays are in the forest, so the starting point of the rule – “NOT J” doesn’t apply. Since the triggering condition of the rule is not satisfied (it applies to situations where Jays *aren’t* in the forest), we don’t care about the right side of the arrow. This rule doesn’t apply, so we can move to the next one. (If you check the contrapositive, you’ll see that the trigger for the contrapositive (“NOT S”) doesn’t apply, but if you know for sure that a rule doesn’t apply, you don’t have to worry about the contrapositive.
Look at the beginning of the actual rule: “If Jays are not in the forest…” Is it the case that Jays are NOT in the forest? No…Jays ARE in the forest. So the rule doesn’t matter at all.
You only have to worry about the right side of the arrow if the condition on the left side of the arrow is met.