1. Renowned economist Harold Carlson makes the following prediction: "The balance of payments will decrease if and only if interest rates remain steady; however, it is not the case that either interest rates will not remain steady or the balance of payments will decrease." What can we say about Carlson's prediction? (B, I)
2. A high school principal made this statement to the school board: "Either music is not dropped from the curriculum or the students will become cultural philistines; furthermore, the students will not become cultural philistines if and only if music is dropped from the curriculum." Assuming the principal is correct, what has she told us about music and the students?
3. Christina and Thomas are having a discussion about their plans for the evening. Christina: "If you don't love me, then I'm certainly not going to have sex with you." Thomas: "Well, that means that if I do love you, then you will have sex with me, right?" Is Thomas correct?
4. Two astronomers are discussing supernovas. Dr. Frank says, "Research has established that if a supernova occurs within ten light-years of the earth, then life on Earth will be destroyed." Dr. Harris says, "Research has also established that either a supernova will not occur within ten light-years of the earth or life on Earth will not be destroyed." Is it possible that both astronomers are correct? If so, what can we determine about the occurrence of a supernova? (S, L)
5. Antonia Martinez, who is running for the state senate, makes this statement: "Either a tax reduction is feasible only if both educational costs do not increase and the welfare program is abolished, or a tax reduction is feasible and either the welfare program will not be abolished or educational costs will increase." What has Martinez told us about taxes, educational costs, and welfare? (T, E, W)
6. Automotive expert Frank Goodbody has this to say about Japanese imports: "If Mitsubishi is the sportiest, then both Toyota is the most trouble-free and Isuzu is not the lowest priced. If Isuzu is the lowest priced, then both Toyota is not the most trouble-free and Mitsubishi is the sportiest." Is it possible that Goodbody is correct in his assessment? If so, what may we conclude about Mitsubishi, Toyota, and Isuzu? (M, T, I)
7. Two stockbrokers are having a discussion. One claims that Netmark will introduce a new product if and only if both Datapro cuts its workforce and Compucel expands production. The other claims that Datapro will cut its workforce, and Compucel will expand production if and only if Netmark introduces a new product. Is it possible that both stockbrokers are right? If so, what have they told us about these companies? (N, D, C)
8. Eric Carson sums up his beliefs about God as follows: "God exists if and only if either life is meaningful or the soul is not immortal. God exists and the soul is immortal. If God exists, then life is not meaningful." Is it possible that Eric's beliefs make sense? (G, L, S)
9. Cindy, Jane, and Amanda witnessed a bank robbery. At trial, Cindy testified that Lefty did not enter the bank, and if Howard pulled a gun, then Conrad collected the money. Jane testified that if Howard did not pull a gun, then Lefty entered the bank. Amanda testified that if Conrad collected the money, then Howard pulled a gun. Is it possible that all three witnesses told the truth? If so, what can we conclude about Lefty, Howard, and Conrad? (L, H, C)
10. Nicole Evans expresses her philosophy as follows: "If the mind is identical to the brain, then personal freedom does not exist and humans are not responsible for their actions. If personal freedom does not exist, then the mind is identical to the brain. Either humans are responsible for their actions or the mind is not identical to the brain. If personal freedom exists, then humans are responsible for their actions." Is it possible that Nicole's philosophy makes sense? If so, what does it say about the mind, personal freedom, and responsibility? (M, P, H)
Use truth tables to obtain the answers to the following exercises. The letters to be used in constructing the truth tables are given in parentheses.