Unit 6 Exercises
1. What rule of inference is used in each of the
following arguments?
- John likes apple pies.  Therefore, John likes apple pies
or icecream.
- Mary likes chocolate and icecream.
  Therefore, Mary likes chocolate.
- If it snows, then the roads are closed;   it snows
.   Therefore, the roads are closed.
- If it snows, then the roads are closed;  
the roads are not closed.  Therefore, it does not snow.
- 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
?
-
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).
-
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).
- 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).
- 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).
-
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).
Answers for these exercises