Question

What are the symbols used in sets and what do they mean?

Answer 1

refer a book on set theory.

Answer 2

Let \(A\) and \(B\) be two sets with universal set \(U\).

\(A\subseteq B \implies \forall x\in A, x\in B\) (everything in \(A\) is in \(B\))

\(A\cup B := \{x\mid x\in A \vee x\in B\}\) (All the stuff in both sets)

\(A\cap B := \{x\mid x\in A \wedge x\in B\}\) (only the stuff that is in both \(A\) and \(B\))

\(A^C=U-C:= \{x\mid x\in U\vee x\notin A\} \) (All the stuff that is not in \(A\))

\(\mathcal{P}(A)=\{S\mid S\subseteq A\}\) (the set of all subsets of \(A\))