For any two sets A and B,A-(A-B) equals | vedclass

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(C) We know that the difference of two sets $A-B = A \cap B^c$. Substituting this into the expression,we get: $A-(A-B) = A-(A \cap B^c)$ Using the pro

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$A \cap B$

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(C) We know that the difference of two sets $A-B = A \cap B^c$. Substituting this into the expression,we get: $A-(A-B) = A-(A \cap B^c)$ Using the property $X-Y = X \cap Y^c$: $= A \cap (A \cap B^c)^c$ Applying De Morgan's Law $(A \cap B^c)^c = A^c \cup (B^c)^c = A^c \cup B$: $= A \cap (A^c \cup B)$ Using the Distributive Law: $= (A \cap A^c) \cup (A \cap B)$ Since $A \cap A^c = \emptyset$: $= \emptyset \cup (A \cap B) = A \cap B$ Therefore,the correct option is $C$.

For any two sets $A$ and $B$,$A-(A-B)$ equals

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