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. For all subests C and D of Y,.
To check the given property whether it is true for all functions or it is false for at least one function
Let be a function from to .
The proof can be divided into two parts.
Part - :
Part - :
Part-1:- The proof of the part- is same as
If , then .
By the definition of inverse image, such that
That means, such that .
By the definition of inverse image,
By the definition of difference of two sets,
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