Diagram the following grouping game rules and make any deductions you can:
- 1. Tova and Roland cannot both be on the team.
- 2. Either Salome or Wendy are on the team.
- 3. If Wendy is on the team, then Tova is also on the team.
Answer
The first rule can be diagrammed as two conditional statements: if T, then not R, and if R, then not T. The second rule can also be diagrammed as two conditional statements: if not S, then W, and if not W, then S. Finally, the third rule can be diagrammed as a conditional statement using the normal rules for conditional diagramming. If you want, for good measure, you can also take the contrapositive of this rule, too. Once we have the individual rules, we can chain them all together by looking for repeating terms. “W” shows up in rules 2 and 3. These rules combine to give us the chain Not S -> W -> T. “T” shows up in rules 1 and 3. That allows us to attach rule one to derive the chain Not S ->W ->T -> Not R. Finally, to be thorough, we can take the contrapositive of the entire chain to get a final deduction: R ->Not W ->Not T -> S.
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