1. Prove that
I will show that each of the two sets is contained in the other.
Let . By definition of the union, for some . Then
Therefore, . This proves that .
Conversely, suppose , so
Note that . Hence, for some ,
For if, on the contrary, for all , then .
Therefore, for some . Hence, , by definition of the union. This proves that .
All action is involved in imperfection, like fire in smoke. - The Bhagavad Gita
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