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