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**detalosi** I am considering the set $\displaystyle \left\{ 1,2,3,4,5,6 \right\}$ and two systems (sets) on $\displaystyle X$ given by:

$\displaystyle \mathcal{G}_{1} =\left\{ \left\{ 1,2,3 \right\}, \left\{2,3,4,5 \right\}, \left\{ 1,6 \right\} \right\}$

$\displaystyle \mathcal{G}_{2} =\left\{ \left\{ 1,4,5 \right\}, \left\{2,3,6 \right\}, \left\{ 4,5,6 \right\} \right\}$

I have to show that $\displaystyle \sigma(\mathcal{G}_{1})=\sigma(\mathcal{G}_{2})$.

I would first like to show that $\displaystyle \mathcal{G}_{1} \subset \sigma(\mathcal{G}_{2})$.

Suggestions to proceed are appreciated.