Housing lotteries are often used by university housing administration to determi

Question

Housing lotteries are often used by university housing administration to determine which students get first choice of dormitory rooms. Use propositional logic and rules of inference to figure out how four students, Bob, Lisa, Jim, and Mary are ranked with respect to one another in the housing lottery. Al that we know about the four students is summarized in the following constraints: 1. Lisa is not next to Bob in the ranking. 2. Jim is ranked immediately ahead of a biology major. 3. Bob is ranked immediately ahead of Jim. 4. One of the women is a biology major. 5. Mary or Lisa is ranked first.

Explanation / Answer

Bob is ranked immediately ahead of Jim (3), and Jim is ranked immediately ahead of a biology major (2). Therefore Jim must be ranked 3rd, and Bob must be ranked 2nd.

One of the women is a biology major (4) is redundant. We already know one of the women is ranked behind Jim.

At this point the women are either 1st or 4th. Lisa is not next to Bob in the ranking (1). She cannot be ranked 1st since Bob is 2nd, therefore Lisa is ranked 4th. There is only one spot remaining, so Mary is ranked 1st.

1st: Mary

2nd: Bob

3rd: Jim

4th: Lisa

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