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