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Foundation of modern math: everything is built from sets and membership ($\in$). Relations and functions are themselves sets of ordered pairs.
Membership: $x \in A$
Subset: $A \subseteq B \iff \forall x., x\in A \Rightarrow x\in B$
Union/intersection/difference: $A\cup B$, $A\cap B$, $A\setminus B$
Cartesian product: $A\times B = {(a,b) : a\in A, b\in B}$
Relation $R$ on $X$: $R \subseteq X\times X$
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