Let X and Y be sets, let A and B be any subsets of X, and let F be a function from X to Y. Fill in the blanks in the following proof that .
The following proof that .
Let X and Y be sets, let A and B be any subsets of X and let F be a function from X to Y, and the incomplete proof of the statement .
X and Y are sets
A and B are subsets of X F is a function from X to Y
Let . By the definition of the union, we then know that
By the definition of the image, there exists (b) some such that .
Since and since :
Thus we then obtain for some and thus y lies in the image of
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