# 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.

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1. Writing a Thesis Statement expresses the main idea of your paper and immediately answers the questions posed by your paper.