The shaded region in the Venn diagram can be | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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?

Similar Questions

Consider the sets $X$ and $Y$ where $X = \{ \text{Ram, Geeta, Akbar} \}$ and $Y = \{ \text{Geeta, David, Ashok} \}$. Find $X \cap Y$.

If $A = \{3, 6, 9, 12, 15, 18, 21\}$,$B = \{4, 8, 12, 16, 20\}$,$C = \{2, 4, 6, 8, 10, 12, 14, 16\}$,and $D = \{5, 10, 15, 20\}$,find $C - A$.

In a school,there are three types of games to be played. Some students play two types of games,but none play all three games. Which Venn diagram$(s)$ can justify the above statement?

If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$,$A = \{2, 4, 6, 8\}$ and $B = \{2, 3, 5, 7\}$,verify that $(A \cup B)^{\prime} = A^{\prime} \cap B^{\prime}$.

Let $A$ and $B$ be two sets in a universal set $U$. Then $A - B$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module