September 26, 2005
1. Decide if the following immediate inference is valid or invalid.
Explain your work. (Consider using the Modern Square of Opposition or Venn diagrams.)
| No fertility drugs are solutions to every problem.
Thus it is false that all fertility drugs are solutions to every problem.
All fertility drugs are solutions to every problem No fertility drugs are solutions to every problem A - - - - - - - - -E |\ /| \ / | \ / | \ / | \ / | \ / | \ / | \ / Note that if we assume the premise | \/ | (E statement: No S are P) is true, /\ the corresponding A statement (All S are P) | / \ | which is in the conclusion can be / \ TRUE or FALSE. | / \ | Therefore the argument is INVALID, for the / \ conclusion does not follow with certainty | / \ | from the premise. / \ | / \ | |/ \| I - - - - - - - - O
Thus the argument is INVALID.
Note. You could also say that the conclusion is an O statement, since it it the negation of the A statement "All fertility drugs are solutions to every problem. Again, the argument is invalid.
2. Translate the following sentences into standard-form categorical propositions.
|Any bank that makes too many risky loans will fail.|
All banks that make too many risky loans are banks
that will fail.
|Unless the sun is shining, a rainbow cannot occur.|
Recall that "Unless" means "if not," so the sentence is
If (the sun is not shining) then (a rainbow cannot occur)
from which we get:
All times the sun is not shining are times a rainbow cannot occur.