The Student Room Group

Big unions and big intersections

Hi,
For the question below I understand the first part fine, but for the over way around the solution makes zero sense, I don’t see how it proves that big intersection G is a subset of big union F. My way of doing it would be to just show that big union F is a member of G and then it is true by def that intersection G is a subset of big union F,

But this solution does something different that makes no sense!
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