Set: distinguishable collection. Element: distinguishable object in the set Element x is in set A: $$$x\in A$$$ ================================================== Cardinality is the number of element which the set has $$$A=\{1,2,3\}$$$ $$$|A| = \text{card}(A) = 3$$$ ================================================== Union of two sets A and B $$$A\cup B$$$ Intersection of two sets A and B $$$A\cap B$$$ ================================================== If set A is sub set of set B: $$$A \subset B$$$ $$$A \subset A$$$ is true If cardinality of A is smaller than B, A is proper subset of B ================================================== Difference set $$$A-B$$$ ================================================== Complement set against entire set $$$\Omega$$$ $$$A^C$$$ $$$A^C=\Omega-A$$$ ================================================== Null set $$$\phi$$$ has none element $$$\phi \subset$$$ all sets Following is true $$$A\cap \phi=\phi$$$ $$$A\cup \phi=A$$$ $$$A\cap A^C=\phi$$$ ================================================== $$$A=\{1,2\}$$$ has 4 number of sub sets $$$A_1=\phi$$$ $$$A_2=\{1\}$$$ $$$A_3=\{2\}$$$ $$$A_4=\{1,2\}$$$ ================================================== If set A has N number of elements, A has $$$2^N$$$ number of sub sets ================================================== Following is true as distribution law $$$A\cup(B\cap C)=(A\cup B)\cap(A\cup C)$$$ $$$A\cap(B\cup C)=(A\cap B)\cup(A\cap C)$$$ ==================================================