Practice Problems - Validity Proofs and English-to-Logic Translations

1. Is the argument valid? Prove your answer.

If Kerry was nominated, then she went to Dallas. If Kerry went to Dallas, she campaigned there. If Kerry campaigned in Dallas, she met the president. Kerry did not meet the president. Either Kerry was nominated or someone else was chosen. Therefore someone else was chosen.

2. Is the argument valid? Prove your answer.

If it rains today, then the ultimate course will be muddy.
The ultimate course is muddy only if the park is closed.
If it snows today, then we will go sledding.
It rains or it snows today.
Therefore the park is closed or it rains today.

3. Is the argument valid? Prove your answer.

Everyone gets sick whenever they walk in the rain or text too much.
There is at least one person who doesn't text too much and doesn't like to watch football games.
Harry doesn't text too much.
Therefore someone doesn't walk in the rain.


4. Translate the following English statements into logical notation.
a) All heroes wear capes. (Universe: set of all people)
b) Some heroes wear capes. (Universe: set of all people)
c) Every train is faster than some cars. (Universe: all vehicles)
d) Some scooters are slower than all bikes, but at least one bike is faster than every scooter.  (Universe: all vehicles)
e) An integer is odd if its square is odd.
f) The sum of an even integer and an odd integer is odd.