Honors Mathematics I
Fall, 2001
Contents
Exercises 1.6
Question 1
Prove that argument A5 on p36 is valid.
Question 2
Prove the following argument is valid:
p  q |
p  r |
 q |
| r |
Question 3
Consider the argument:
| If the King racts badly to The Moustrap then he murdered his brother. |
| If the King murdered his brother then the ghost is telling the truth. |
| The king reacted badly to The Mousetrap. |
| The ghost is telling the truth. |
Write this symbolically and prove that it is valid.
Question 4
Consider the following argument:
| If he knew about it, he is culpable. |
| If he did not know about it, he is incompetant. |
| If he is culpable, he should be sacked. |
| If he is incompetent, he should be sacked |
| He should be sacked. |
Is it valid? If so, prove that it is true.
Question 5
Consider the following passage:
If capital investment remains constant, then government spending will increase or unemployment will result. If government spending will not increase, then taxes can be reduced. If taxes can be reduced and capital investment remains constant, then unemployment will not result. Hence government spending will increase.
Is this a valid argument? If so, prove it.
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