The shaded region in the Venn diagram can be | vedclass

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Question

(C) The shaded region consists of elements that are in $A$ but not in $B$,elements in $C$ but not in $B$,and the intersection $A \cap B \cap C$.This c

Vedclass · Accepted Answer

$(A \cup C)\cap (A^C \cup B^C )\cap(A^C \cup C^C )\cap(B^C \cup C^C) \cup(A \cap B \cap C)$

Vedclass · Answer

(C) The shaded region consists of elements that are in $A$ but not in $B$,elements in $C$ but not in $B$,and the intersection $A \cap B \cap C$.This can be expressed as $(A \setminus B) \cup (C \setminus B) \cup (A \cap B \cap C)$.Using set identities,$(A \setminus B) = A \cap B^C$ and $(C \setminus B) = C \cap B^C$.Thus,the region is $(A \cap B^C) \cup (C \cap B^C) \cup (A \cap B \cap C)$.Simplifying this,we get $(A \cup C) \cap B^C \cup (A \cap B \cap C)$.Evaluating the given options,option $C$ represents the correct set operation for the shaded region.

The shaded region in the Venn diagram can be represented by which of the following?

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