July 26, 1996
1(a) Prove A =
(b) Find all the subsets of {
}. 2 (a) Formalize the argument given below using the following symbols.
B: It is a bomb.
M: It is a missile.
F: It is a mechanical failure.
C: Chemicals are detected.
The argument is
It is a bomb, missile or mechanical failure. If it is a bomb, chemicals will be detected. But no chemicals have been detected. A mechanical failure of that nature can not happen. Therefore it must be a missile.
(b) Prove the validity of the resulting form i.e. the statement following "Therefore".
3(a) Inductively define the set of numbers that are divisible by 3.
(b) Write a recursive procedure to test whether or not a given number is divisible by 3 based on your definition of (a).
4. Prove by induction
= n(n+1)(2n+1)/6