Problem Solving Strategies Crossing The River With Dogs

Their statements then can be formalized as \begin (1) \;\;\; T(d) & \;\equiv\; s=r \;\lor\; s=c \ (2) \;\;\; T(r) & \;\equiv\; s \ne v \;\land\; s \ne r \ (3) \;\;\; T(c) & \;\equiv\; \lnot T(r) \;\land\; \lnot T(d) \ (4) \;\;\; T(b) & \;\equiv\; (T(r) \;\not\equiv\; T(d)) \ (5) \;\;\; T(v) & \;\equiv\; \lnot T(b) \ \end Finally, we are given that exactly 3 of $\; T(d), T(r), T(c), T(b), T(v)\;$ are true.

Since $(5)$ says that $\; T(b)\;$ and $\; T(v)\;$ are each others' opposites, we can use this to go from "exactly 3 of ..." to "exactly 1 of ...": \begin & \text T(d), T(r), T(c), T(b), T(v) \text \ \equiv & \;\;\;\;\;\text \ & \text T(d), T(r), T(c) \text \ \equiv & \;\;\;\;\;\text \ & \text \lnot T(d), \lnot T(r), \lnot T(c) \text \ \Rightarrow & \;\;\;\;\;\text \ & \lnot T(d) \;\equiv\; \lnot T(r) \;\equiv\; \lnot T(c) \ \equiv & \;\;\;\;\;\text \ & \lnot T(d) \;\equiv\; \lnot T(r) \;\equiv\; T(r) \;\lor\; T(d) \ \equiv & \;\;\;\;\;\text \ & T(d) \;\equiv\; T(r) \;\equiv\; T(r) \;\lor\; T(d) \ \equiv & \;\;\;\;\;\text \ & T(r) \;\land\; T(d) \ \equiv & \;\;\;\;\;\text \ & s \ne v \;\land\; s \ne r \;\land\; (s=r \;\lor\; s=c) \ \equiv & \;\;\;\;\;\text \ & s \ne v \;\land\; s \ne r \;\land\; s=c \ \equiv & \;\;\;\;\;\text \ & s=c \ \end Therefore Charlton slept.

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Visit Stack Exchange One of the five members of a company's board of directors was suspected of sleeping during a board meeting.

It was known that only one board member had actually slept, but no one (except the five members) knew who it was.

Problem Solving Strategies Crossing The River With Dogs-65Problem Solving Strategies Crossing The River With Dogs-65

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