Symbolize the following arguments showing all the logical
connectives used. Circle the letter in each atomic sentence that you will
use in your symbolization.
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1. Georgia will play Tennessee again this fall. Georgia will win the SEC championship only if they win that game. But a necessary and sufficient condition for Georgia to go to the Sugar Bowl is that they win the SEC championship. So if Georgia wins the Tennessee game, they will go to the Sugar Bowl.
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2. Neither Russia nor China will support a U.S. attack on Iraq. There will not be a U.N. ultimatum on arms inspection in Iraq unless either Russia or China supports a U.S. attack on Iraq. If there is no U.N. ultimatum on arms inspection in Iraq and the U.S. attacks Iraq anyway, then Saudi Arabia will not allow the U.S. to use bases within its borders. So either the U.S. will not attack Iraq or Saudi Arabia will not allow the U.S. to use bases within its borders.
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3. Only if gravity deflected light would stars appearing on opposite sides of the sun during a total eclipse appear closer together than at other times. But if light is deflected by gravity, light must have mass. So unless light has mass, stars appearing on opposite sides of the sun during a total eclipse will not appear closer together than at other time.
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4. The recession will end soon if and only if more jobs are created and inflation remains low. If interest rates remain low, inflation will remain low. Consumer confidence will improve only if more jobs are created. So since interest rates will remain low, either consumer confidence will not improve or the recession will end soon.
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5. Mary took geometry and calculus in high school, but Linda didn't take geometry or calculus. If they had both gone to Lincoln High, they would both have taken calculus. So they didn't both go to Lincoln High.
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6. Henry didn't fire the gun. Otherwise, he would have had gun powder residue on his hands. If he had gun powder residue on his hands, the paraffin test would have revealed it. But the paraffin test was negative.
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7. A necessary condition for the car to start is a good battery. If the lights work and the horn works, then the battery is good. The lights and horn work. So the car will start.
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8. If determinism is true, we can not do other than we do, hence we are not responsible for what we do. If indeterminism is true, then human actions are random, hence not free, hence we are not responsible for what we do. Either determinism or indeterminism is true. Therefore, we are not responsible for what we do.
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9. People are different from animals either in kind or in degree. If we are different in kind, then there should be at least one characteristic we obviously have that animals don't. There is no obvious difference; therefore we must be different in degree. But if we are only different from animals in degree then we're essentially just animals.
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10. I'm buying my mother a new watch for Christmas; but if I buy the watch, I can't afford the table saw my father has been wanting. If I can't get him the table saw, I can still get him books or a new jacket. If I get him books, I can afford a gift for my favorite aunt. If I buy him a jacket, I cannot. I want to give my aunt a Christmas present.
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