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- Wed Aug 20, 2014 11:00 pm
#40566
Setup and Rule Diagram Explanation
This is a Grouping: Partially Defined game.
The game scenario establishes that at least four employees will be selected from a group of eight employees:
With a group being selected, and order not important, this is a Grouping game. Because the research team must contain at least four employees, but could contain more, the game is Partially Defined. Let’s examine the rules, which, unsurprisingly, are all conditional.
The first rule is actually two rules-in-one, and establishes that M cannot be on the team with O or with P. For the sake of clarity, write these relationships out separately:
Note that this rule automatically eliminates all eight employees from being selected for the team. If M is selected, the maximum number of employees that could be on the team at this point in our analysis is six. If M is not selected, the maximum at this point is seven (all employees except M).
The second rule indicates that if S is selected, then both P and T are selected:
Because P appears in both the first and second rules, we can link those rules together via the following chain (T is dropped for the moment since it is superfluous to this inference):
Resulting in the following inference:
Side note: drawing out the:
connection is not necessary in order to draw the inference. After diagramming the first two rules, you can visually link the rules and then write out just the:
inference.
The third rule indicates that if W is selected, then both M and Y are selected:
This rule can be connected to the other rules to draw several inferences. First, combining the third rule and the first rule creates the following chains:
The two chains respectively create the following two inferences:
The inference created by the first and second rules can also be recycled and combined with the third rule via the following chain:
Which then results in the following inference:
From these rules and inferences you can see that M and W are both powerful variables. If M is selected, then O, P, and S are eliminated. If W is selected, then M and Y must be selected, and O, P, and S are eliminated. In each instance, then, the maximum number of employees selected for the team is five.
Combining all of the prior information, and the fact that Z is a random, leads to the final diagram for the game:
Numerically, the research team can only have 4, 5, or 6 members:
1, 2, or 3 members can never occur because 4 is the minimum stipulated in the game scenario.
8 members can never be selected because of the first rule.
7 members can never occur because either M or W would have to be selected in the group of 7, and as detailed earlier they limit the total number of members to 5.
6 could be selected by eliminating both M and W from the team, and choosing all six of the remaining employees.
This is a Grouping: Partially Defined game.
The game scenario establishes that at least four employees will be selected from a group of eight employees:
With a group being selected, and order not important, this is a Grouping game. Because the research team must contain at least four employees, but could contain more, the game is Partially Defined. Let’s examine the rules, which, unsurprisingly, are all conditional.
The first rule is actually two rules-in-one, and establishes that M cannot be on the team with O or with P. For the sake of clarity, write these relationships out separately:
Note that this rule automatically eliminates all eight employees from being selected for the team. If M is selected, the maximum number of employees that could be on the team at this point in our analysis is six. If M is not selected, the maximum at this point is seven (all employees except M).
The second rule indicates that if S is selected, then both P and T are selected:
Because P appears in both the first and second rules, we can link those rules together via the following chain (T is dropped for the moment since it is superfluous to this inference):
Resulting in the following inference:
Side note: drawing out the:
connection is not necessary in order to draw the inference. After diagramming the first two rules, you can visually link the rules and then write out just the:
inference.
The third rule indicates that if W is selected, then both M and Y are selected:
This rule can be connected to the other rules to draw several inferences. First, combining the third rule and the first rule creates the following chains:
The two chains respectively create the following two inferences:
The inference created by the first and second rules can also be recycled and combined with the third rule via the following chain:
Which then results in the following inference:
From these rules and inferences you can see that M and W are both powerful variables. If M is selected, then O, P, and S are eliminated. If W is selected, then M and Y must be selected, and O, P, and S are eliminated. In each instance, then, the maximum number of employees selected for the team is five.
Combining all of the prior information, and the fact that Z is a random, leads to the final diagram for the game:
Numerically, the research team can only have 4, 5, or 6 members:
1, 2, or 3 members can never occur because 4 is the minimum stipulated in the game scenario.
8 members can never be selected because of the first rule.
7 members can never occur because either M or W would have to be selected in the group of 7, and as detailed earlier they limit the total number of members to 5.
6 could be selected by eliminating both M and W from the team, and choosing all six of the remaining employees.
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