[emilia]

So i am confused on the (not)J –> S rule. I take the contrapositive of that, and it reads (not)S –> J. I don’t understand how they could both be in the forest (question 7)
It seems like either one or the other is in the forest?

[dannypearlberg]

This is definitely an important type of rule to understand: not J -> S means that you can’t have both J and S out, because when J is out then S is in, and when S is out then J is in. However, just because you can’t have both J and S out, this doesn’t preclude J and S both being IN. Given the rule and its contrapositive, if J is in then S could be either in or out. Likewise, if S is in then J could be either in or out. So the only possibility that the rule excludes is the possibility of both J and S being out.

A similarly important type of rule to understand: J-> not S means that you can’t have both J and S in, because when J is in then S is out, and (from the contrapositive) when S is in then J is out. However, just because you can’t have both J and S in, this doesn’t preclude J and S both being OUT. Given the rule and its contrapositive, if J is out then S could be either in or out. Likewise, if S is out then J could be either in or out. So the only possibility that this rule excludes is the possibility of both J and S being in.

Hope that helps 🙂

[LSAT Dan]

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.

[dannypearlberg]

Awesome addition Dan 🙂

[emilia]

Thank you both for the clarifying explanations. I’m beginning to understand the logic behind the rule. I think the reason I confused the not J–> S rule is because the first rule states if H–> not G. They seem so similar so I applied the first rule logic to the last, which obviously is wrong.

Can someone explain the difference between these two rules in comparison?
I appreciate it!

[dannypearlberg]

If H-> not G works the same way as my hypothetical example above of if J->not S. So, if not J->S means that J and S can’t both be out, but they could both be in. If H->not G means that H and G can’t both be in, but they could both be out.