ABSTRACT
Sets are usually denoted by letters and the elements of a set are listed in eurlv brackets or by specifying the property that its elements (and its elements only) satisfy. For example,
A = {1, 2, 3} = {x : x is a positive integer <= to 3 }
If a is an element of the set A then we write
a E A
a & A means a is not an element of A, The number of elements in a finite set A is denoted by |A|, An empty set, denoted by 0, is the set with no elements, and obviously |0 | = 0,
A C B
m eans every elem ent of A is also an elem ent o f B, A is called a subset of B and B a superse t of A, A = B m eans A C B and
A = B <=> A C B and B ( A
0 = 6 means the symbols o and 6 represents the same element. By definition, A C A and 0 C A for any set A, A nonempty set A is called a proper subset of B if A C B but A ^ B .
