Winter Term 2000
The World According to Mathematics
No kitten without a tail will play with a gorilla.
Kittens with whiskers always love fish.
No teachable kitten has green eyes.
No kittens have tails unless they have whiskers.
Write the statements in (a) in symbolic form p‡q.
Using the Law of Syllogism, [(p‡q) and (q‡r)] implies (p‡r), reorganize the
symbolic statements in (b) and deduce the one conclusion that follows from
these statements. [For example, if two of your statements are p‡q and q‡r,
then you can deduce that p‡r. Continue in this way with the other statements.]
Write your symbolic answer in (c) in words again.
Determine all cases in which the conclusion is false, and show that in each case at
least one premise is false.
Explain why the following sentence is self-contradictory, neither true nor false:
Here is a logical paradox formulated by Jules Richard (a Frenchman) in 1903:
of the whole numbers. First, we would have to list the
characteristics—characteristics such as even, odd, multiple of 7, or perfect square.