1. If sports-shoe manufacturers decline to use kangaroo hides in their products, then Australian hunters will cease killing millions of kangaroos yearly. It is not the case that both Australian hunters will cease killing millions of kangaroos yearly and the kangaroo will not be saved from extinction. Therefore, if sportsshoe manufacturers decline to use kangaroo hides in their products, then the kangaroo will be saved from extinction. (D, C, S)

2. If there is a direct correlation between what a nation spends for health care and the health of its citizens, then America has the lowest incidence of disease and the lowest mortality rates of any nation on Earth. But America does not have the lowest mortality rates of any nation on Earth. Therefore, there is not a direct correlation between what a nation spends for health care and the health of its citizens. (C, D, M)

3. It is not the case that strict controls exist on either the manufacture or the sale of handguns. Therefore, if strict controls exist on the sale of handguns, then the use of handguns in the commission of crimes has decreased. (M, S, U)

4. If birth-control devices are made available in high school clinics, then the incidence of teenage pregnancy will decrease. Therefore, if both birth-control information and birth-control devices are made available in high school clinics, then the incidence of teenage pregnancy will decrease. (D, P, I)

5. If Congress enacts a law that either establishes a religion or prohibits the free exercise of religion, then that law is unconstitutional. Therefore, if Congress enacts a law that establishes a religion, then that law is unconstitutional. (E, P, U)

6. If selecting a Supreme Court justice creates intense political upheaval and extreme efforts are expended to block judicial candidates, then Supreme Court rulings are contaminated with political bias. Selecting a Supreme Court justice creates intense political upheaval. Therefore, if extreme efforts are expended to block judicial candidates, then Supreme Court rulings are contaminated with political bias. (S, E, C)

7. If grade-school children are assigned daily homework, then their achievement level will increase dramatically. But if grade-school children are assigned daily homework, then their love for learning may be dampened. Therefore, if grade-school children are assigned daily homework, then their achievement level will increase dramatically but their love for learning may be dampened. (G, A, L)

8. If two black holes collide, then Einstein's general theory is proven true and gravitational waves are propagated throughout the universe. Either two black holes collide, or space-time is distorted and Einstein's general theory is proven true. Therefore, Einstein's general theory is proven true. (T, E, G, S)

9. If parents are told that their unborn child has Tay-Sachs disease, then if they go ahead with the birth, then they are responsible for their child's pain and suffering. Therefore, if parents are not responsible for their child's pain and suffering, then if they go ahead with the birth, then they were not told that their unborn child had Tay-Sachs disease. (T, G, R)

10. Vitamin E is an antioxidant and a useless food supplement if and only if it does not reduce heart disease. It is not the case either that vitamin E does not reduce heart disease or is not an antioxidant. Therefore, vitamin E is not a useless food supplement. (A, U, R)

Translate the following arguments into symbolic form and then use the eighteen rules of inference to derive the conclusion of each. Use the translation letters in the order in which they are listed.