Question #779

[AlexY297]

Hello, I'm not sure I understand the diagram completely, particularly the second half of the diagram with I, K and J. Then below it says, "If exactly two are in, it must be true that..."

Can someone explain this please?


Thank you, Alex.

[Laura Damone]

Hi there!

This is a Logic Chain diagram for an In/Out grouping game. If you're not familiar with that type of diagram yet, you can check out this quickie introduction on our Youtube channel: https://www.youtube.com/watch?v=wH1PgKowt50

In the diagram for q779, we can see the following relationships:

If H is in, I is out.

If I is in, H is out.

If J is in, K is in, and if K is in, I is in.

If I is out, K is out, and if K is out, J is out.

The question stem asks us what must be true if there are exactly two elements in. Since there are 4 elements total, that means there are also 2 elements out.

Well, since H and I can't be in together, we know at least one of them is out. But if I is out, so are K and J. That's too many elements out. So, I can't be out, and must therefore be in. I being in forces H out, so now we have one in each group. That leaves K and J. One must be in and the other out. But if J is in, K is in with it, and if K is out, J is out, too. We can't have that, so we need to place K in and J out, proving the correct answer: J is out.

Hope this helps!