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Universal Relations

What is a set...

Question

What is a set and list all formulas of set.

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Solution

A set is a collection of objects that have something in common or follow a rule. The objects in the set are called its elements. Set notation uses curly braces, with elements separated by commas.

For example, Q = {2, 4, 6, 8}

Some of the common symbols are listed with examples below:
$\begin{matrix} S y m b o l & M e a n i n g & E x a m p l e {} & S e t : a c o l l e c t i o n o f e l e m e n t s & {1, 2, 3, 4} A \cup B & U n i o n : i n A o r B (o r b o t h) & C \cup D = {1, 2, 3, 4, 5} A \cap B & I n t e r s e c t i o n : i n b o t h A a n d B & C \cap D = {3, 4} A \subseteq B & S u b s e t : A h a s s o m e (o r a l l) e l e m e n t s o f B & {3, 4, 5} \subseteq D A \subset B & P r o p e r s u b s e t : A h a s s o m e e l e m e n t s o f B & {3, 5} \subset D A / \subset B & N o t a S u b s e t : A i s n o t a s u b s e t o f B & {1, 6} / \subset C A \supseteq B & S u p e r s e t : A h a s s a m e e l e m e n t s a s B, o r m o r e & {1, 2, 3} \supseteq {1, 2, 3} A \supset B & P r o p e r S u p e r s e t : A h a s B^{'} s e l e m e n t s a n d m o r e & {1, 2, 3, 4} \supset {1, 2, 3} A / \supset B & N o t a S u p e r s e t : A i s n o t a s u p e r s e t o f B & {1, 2, 6} / \supset {1, 9} A^{c} & C o m p l e m e n t : e l e m e n t s n o t i n A & D^{c} = {1, 2, 6, 7} W h e n U = {1, 2, 3, 4, 5, 6, 7} A - B & D i f f e r e n c e : i n A b u t n o t i n B & {1, 2, 3, 4} - {3, 4} = {1, 2} a \in A & E l e m e n t o f : a i s i n A & 3 \in {1, 2, 3, 4} b \in A & N o t e l e m e n t o f : b i s n o t i n A & 6 \in {1, 2, 3, 4} ϕ & E m p t y s e t = {} & {1, 2} \cap {3, 4} = ϕ \end{matrix}$

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