A - (A - B) is equal to: | vedclass

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Question

(B) We know that the set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$. Mathematically,$A - B = A \cap B^c$.Subs

Vedclass · Accepted Answer

$A \cap B$

Vedclass · Answer

(B) We know that the set difference $A - B$ is defined as the set of elements that are in $A$ but not in $B$. Mathematically,$A - B = A \cap B^c$.Substituting this into the expression $A - (A - B)$,we get:$A - (A \cap B^c)$Using the property $X - Y = X \cap Y^c$,we have:$A \cap (A \cap B^c)^c$Applying De Morgan's Law,$(A \cap B^c)^c = A^c \cup (B^c)^c = A^c \cup B$.So,the expression becomes:$A \cap (A^c \cup B)$Using the distributive law of intersection over union:$(A \cap A^c) \cup (A \cap B)$Since $A \cap A^c = \emptyset$ (the empty set):$\emptyset \cup (A \cap B) = A \cap B$.Therefore,$A - (A - B) = A \cap B$.

$A - (A - B)$ is equal to:

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