Which one of the following is an acceptable selection of fish and plants for the aquarium?
joaquin-acunaApril 6, 2020
Game Setup
Hi there; how this game may not be an in-out game where we have five variables in (3 fishes and 2 plants) and four variables out (2 fishes and 2 plants)? if it could be diagrammed as in-out game, how would you diagram and place the first rule into the game setup? To me the first rule is a "not both" rule, and it should read: G --- not H & not Y (and its contrapositive), meaning that at least one of either G or H&Y must be out, or possibly both. Other question, is Y is in, doest that mean that H must be in too? Thank you!
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We will select 3 of 5 fish (GHJKL) and 2 of 4 plants (WXYZ). Therefore, some variables will be selected and some variables will be left out for each of our two groups. We do not necessarily need to diagram the variables that are left out, but you can mark these if you find doing so helpful.
The first rule tells us: G -> not H and not Y H or Y -> not G This means that we cannot have G, H, and Y all selected at the same time. Your understanding of this as a "not both" rule is correct. We should mark this with our rules, but we do not place it on our diagram yet.
Based off our rules, we do not know that H must be in if Y is in. However, we will see that this ends up being true in practice. To see this, let's try to put Y in without H. Our three fish must be J, K, and L. This is because we cannot have G and Y both in (Rule #1), and we do not want H in with Y for the purposes of what we're trying to prove. W must be in if J is in (Rule #3) and X must be in if K is in (Rule #4). These take up the two plant spots, leaving no room for Y. Therefore, it is impossible to have Y in without H also in. This point is also affirmed in question #16 of this game.
Here is a full game set up:
F: GHJKL P: WXYZ
F: __ __ __ P: __ __
Rule #1: G -> not H and not Y H or Y -> not G
Rule #2: H -> K not K -> not H
Rule #3: J -> W not W -> not J
Rule #4: K -> X not X -> not K
The only deduction we can make is based on the contrapositive of Rule #2. If K is out and H is out, the three fish that must be in are G, J, and L. Rule #3 tells us that if J is in, W must be in. Rule #1 tells us that if G is in, Y cannot be in. This gives us a scenario of:
F: G J L P: W (X/Z)
Does that make sense? Please let us know if you have any other questions!
joaquin-acunaJune 8, 2020
thank you for your help with this. Great explanation.
Anthony-ResendesAugust 27, 2020
I barley started the course last Saturday, So I haven't had a chance to watch all the videos but thought I would do a grouping game, for some odd reason I have come to enjoy games, and I'm currently half way through the sufficient and necessary video. So does a "cannot" introduce a sufficient condition and the necessary condition follows??
