所屬科目：中山◆資工◆離散數學與演算法
2. Verify that , for primitive statements , and .
(a) Wiite a quantified statement to express the proper subset relation .
(b) Negate the result in part (a) to determine when .
4. (a) Consider an chessboard. It contains eighty-one squares and one square. How many squares?
(b) Now consider an chessboard for some fixed . ForI , how many squares are contained in this chessboard?
5. Let be a set of five positive integers the maximum of which is at most 9. Prove that the sums of the elements in all the nonempty subsets of S cannot all be distinct.
6. (a) Fermat's Theorem. If is a prime, prove that for each .
(a).
(b)
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, for primitive
statements 
, and 
.
.
.
chessboard. It contains eighty-one 
squares and one 
square.
How many 
squares?
chessboard for some fixed 
. ForI 
, how many 
squares are contained in this chessboard?
be a set of five positive integers the maximum of which is at most 9. Prove that the sums
of the elements in all the nonempty subsets of S cannot all be distinct.
is a prime, prove that 
for each 
.
.