Group Games Questions - - Question 2

If the planting committee consists of F, H, L, and M, and if the trails committee consists of G, H, and J, then K cou...

Anevay December 26, 2019

Why not F?

Why can't F be replaced by K? I understand why the answer is G, but I also thought it could be F.

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Skylar December 27, 2019

@Anevay, happy to help.

F cannot be replaced by K because of our third rule, which says "If K is on a committee, J must also be on that committee," or K -> J. If we were to replace F with K, the planting committee would consist of K, H, L, M. This would violate Rule #3 because we have K on a committee without J.

Does that make sense? Let us know if you have any other questions and best of luck with your studies!

Anevay December 27, 2019

Yes, thank you! I guess I was not applying the rules both ways and thought J could be on a committee without K.

Skylar December 28, 2019

@Anevay, I'm glad that makes more sense!

Just to clarify, J can be on a committee without K (as is the case in the original trails committee we were given in this question). The rule "If K is on a committee, J must also be on that committee" is written as K -> J and the contrapositive is NOT J -> NOT K. Since J is never the Sufficient condition, it can exist on a committee without K. However, K cannot exist on a committee without J, which is why (A) is incorrect.