In 41-49 let X and Y be sets, let A and B be any subsets of X, and let C and D be any subsets of Y. Determine which of the properties are true for every fubnction F from X to Y of the properties are ture for every function F from X to Y and which are false for at lest for at lest one functions F from X to Y. Justify your answer.
To check the given property whether it is true for all functions or it is false for at least one function
A and B are any two subsets of a set X.
Let be a function from
Since so by definition of image of a set, we have for some .
This implies that for some
So, we have for some for some
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