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Winter Term 2000

The World According
to Mathematics

in
Wonderland.

2.

3.

4.

5.

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.

(b)

(c)

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.