This is an explanation of the second logic game from Section IV of LSAT 33, the December 2000 LSAT.
Bird-watchers are trying to find out what kind of birds are present on a certain forest. The six birds are grosbreak, harrier, jay, martin, shrike, and wren (G, H, J, M, S, W). The rules allow you to determine what birds can be present together.
This is an in-out grouping game. Like pure sequencing games, this is a very important type of game to learn. Once you know how to do one of these games well, you can do all of them.
There are two ways to set up these games. A slow way, and a fast way that makes you actively think about the rules.
The slow way is to draw out each rule individually, and draw its contrapositive. People think this helps them avoid mistakes. But as an LSAT tutor, I get to watch people try this method. They usually get lost in a sea of diagrams.
Worse, they don’t think about the rules as they draw them, or how the rules fit together. They rarely connect everything into a larger diagram, and the game goes badly.
The fast way is to start with one rule, and add each new rule to the diagram. In almost all in-out grouping games, you can join the rules into one diagram. This process forces you to think about the rules and actively learn the game.
Let me show you how that works. Here’s the first rule:
If H is in, G is out. The next rule joins on this directly: if J or M are in, H is in too.
So if, for example, J is in, then H is in and G is out. We don’t know about M, because J and M aren’t connected.
The next rule requires you to take the contrapositive. If W is in, G is in. So if G isn’t in, then W can’t be in either:
This can also be added directly to the diagram. You can always join a necessary condition to a sufficient condition if the term is the same (e.g. “not G”).
We can also take the contrapositive of the last rule and add it to the diagram. If J is out, S is in.
Contrapositives shouldn’t be hard. You just switch the terms, and put a line through them (or remove a line).
So if S is out, J is in:
This can be added to the left of the diagram:
Voila! A full diagram. Every rule is there.
A note on how to read this diagram: you can only go left to right. So If J is in, then H is in, and GW are out.
But you don’t know anything about S, because S is to the left of J. Your diagram doesn’t tell you what happens to S if J is in. S could be in if J is in.
Taking the contrapositive of the main diagram
You’ll want to take the contrapositive of the diagram. Then you’ll have two large diagrams that tell you everything.
Start by reversing everything, then negating it. Negating means putting a line through everything, or removing a line.
So we start with W being in. This forces G in, and this causes H to be out:
It’s important that “or” becomes “and” in a contrapositive, and vice versa. I’ll explain why with an example. Suppose I say:
“If you have a boy or a girl, you’re a parent”.
The contrapositive is:
“If you’re not a parent, you don’t have a boy and you don’t have a girl”.
Jays and Shrikes can both be in
A quick note on the rules about S and J. They confuse most people that try this game. Here’s the rule again, and the contrapositive:
If one is out, the other is in. That does not mean that if one is in, the other is out! They’re completely different things.
This is the biggest point of confusion in this game, and it comes from not fully understanding the diagrams. You must read them left to right.
So look at the diagrams above. If J is out, the arrow tells you S is in. But if S is in, the arrow doesn’t tell you anything. You can’t go left.
At least one of S and J will be in, but they could both be in.
H and G have the opposite relationship. At least one will be out, and they might both be out. If H is in, G is out, and vice-versa. But they could both be out.
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