Unit 6 Exercises

1. What rule of inference is used in each of the following arguments?

1. John likes apple pies.  Therefore, John likes apple pies or icecream.
2. Mary likes chocolate and icecream.   Therefore, Mary likes chocolate.
3. If it snows, then the roads are closed;   it snows .   Therefore, the roads are closed.
4. If it snows, then the roads are closed;   the roads are not closed.  Therefore, it does not snow.
5. To go to Tahiti, one must fly or take a boat;   there is no seat on any flight to Tahiti this year.  Therefore, one must take a boat to go to Tahiti this year.

2. Express the following arguments using the symbols indicated. What rules of inference are used in each of them ?

1. If the teens like it, then the sales volume will go up;   Either the teens like it or the store will close;   The sales volume will not go up.   Therefore, the store will close.
Symbols to be used: The teens like it (T). The sales volume will go up (S). The store will close (C).
2. It is not the case that if there is not a lot of sun, then there is enough water, nor is it true that either there is a lot of rain or the crop is good. Therefore, there is not enough water and the crop is not good.
Symbols to be used: There is not a lot of sun (S). There is enough water (W). There is a lot of rain (R). The crop is good (C).
3. If flowers are colored, they are always scented;   I don't like flowers that are not grown in the open air;   All flowers grown in the open air are colored .  Therefore, I don't like any flowers that are scentless.
Symbols to be used: Flowers are colored (C). Flowers are scented (S). I like flowers (L). Flowers are grown in the open air (O).
4. No animals, except giraffes, are 15 feet or higher;   There are no animals in this zoo that belong to anyone but me;   I have no animals less than 15 feet high.  Therefore, all animals in this zoo are giraffes.
Symbols to be used: Animals are giraffes (G). Animals are 15 feet or higher (F). Animals are in the zoo (Z). Animals belong to me (M).
5. Bees like red flowers, or my hat is red and bees like hats;   However, my hat is not red, or bees don't like hats but they like red flowers. Therefore bees like red flowers.
Symbols to be used: Bees like red flowers (R). My hat is red (H). Bees like hats (L).