July 25, 1995
1 (a) Prove A - B =
(b) Simplify
. Hint: First draw a Venn diagram and take a guess at what it is equal to. Then derive your guess.
2 (a) Formalize the argument given below using the following symbols.
C: The conclusion of this argument is true.
P: The premises of this argument are all true.
S: This argument is sound.
V: This argument is valid.
The argument is
If this argument is valid and all its premises are true, then it is sound. If it is sound, then its conclusion is true. All its premises are true. Therefore, if this argument is valid, then its conclusion is true.
(b) Prove the validity of the resulting form i.e. the statement following "Therefore".
3. Inductively define
, which is denoted by 
,
for every natural number n > 0. 4. Prove by induction
= 
for every natural number n > 0. Here
= 
and
=
. Hint: You may use
= 
for two sets A and B as given.