\(A_{1}=\left\{ a,b\right\} ,A_{2}=\left\{ a,c\right\} ,\Lambda=\left\{ 1,2\right\} \)とすると、
\begin{align*} \bigcup_{\lambda\in\Lambda}A_{\lambda} & =\bigcup_{\lambda\in\left\{ 1,2\right\} }A_{\lambda}\\ & =\left\{ x;\exists\lambda\in\left\{ 1,2\right\} ,x\in A_{\lambda}\right\} \\ & =\left\{ x;x\in A_{1}\lor x\in A_{2}\right\} \\ & =\left\{ x;x\in\left\{ a,b\right\} \lor x\in\left\{ a,c\right\} \right\} \\ & =\left\{ a,b,c\right\} \end{align*} \begin{align*} \bigcap_{\lambda\in\Lambda}A_{\lambda} & =\bigcap_{\lambda\in\left\{ 1,2\right\} }A_{\lambda}\\ & =\left\{ x;\forall\lambda\in\left\{ 1,2\right\} ,x\in A_{\lambda}\right\} \\ & =\left\{ x;x\in A_{1}\land x\in A_{2}\right\} \\ & =\left\{ x;x\in\left\{ a,b\right\} \land x\in\left\{ a,c\right\} \right\} \\ & =\left\{ a\right\} \end{align*} となる。