TABLE OF CONTENTS Let us recall some results related to the algebra sets. The main operations on sets are "and", "or" or "+", and "not", which are denoted by ?, ?, or c respectively. These operations produce new sets. The Venn diagram of these operations is drawn in Figure 1.1.
The following table summarizes the main properties of the operations on sets.
| A ? B ? B c ? A c |
| AB = BA and A ? B = B ? A |
| ( AB) C = ( A) BC and ( A ? B) ? C = A ? ( B ? C) |
| A( B ? C) = AB ? AC and A ? BC = ( A ? B) ( A ? C) |
| ( AB) c = A c ? B c, ( A ? B) c = A cB c and A ? B = A + A cB |
| ( ? n i=1 A i) c = ? n i=1 A c i, ( ? n i=1 A i) c = ? n i=1 A c i. |
| ? n i=1 A i = A 1 ? ( A c 1 ? ( A 2) ? |
