\[\begin{align} \mbox{Union: } & A\cup B = \{x\mid x\in A \mbox{ or } x\in B\} \\ \mbox{Concatenation: } & A\circ B = \{xy\mid x\in A \mbox{ and } y\in B\} \\ \mbox{Star: } & A^\star = \{x_1x_2\ldots x_k \mid k\geq 0 \mbox{ and each } x_i\in A\} \\ \end{align}\]