Question

if n(A-B)=10 n( B-A) =8 n (AnB)=3 then find n (AuB) by using even venn diagram​

Answer 1

Given,

$\[\begin{array}{l}n\left( {A - B} \right) = 10\\n\left( {B - A} \right) = 8\\n\left( {A \cap B} \right) = 3\end{array}\]$

To find,

$\[n\left( {A \cup B} \right)\]$

Solution,

Know that the formula to calculate $\[n\left( {A \cup B} \right)\]$ is$\[n\left( {A - B} \right) + n\left( {B - A} \right) - n\left( {A \cap B} \right).\]$

Apply values.

Therefore,

$\[\begin{array}{l} \Rightarrow 10 + 8 - 3\\ \Rightarrow 18 - 3\\ \Rightarrow 15\end{array}\]$

Hence, the value of $\[n\left( {A \cup B} \right)\]$ is$\[15\]$.

Answer 2

n(A U B)  =  21 if n(A-B)=10 n( B-A) =8 n (A∩ B)=3

Given:

• n(A-B) = 10
• n(B - A) = 8
• n (A ∩ B) = 3

To Find :

• n(A U B)

Solution:

Venn Diagram is used to show relationship between two or more sets.

n(A - B) = n(A) - n (A ∩ B)

n(B - A) = n(B) - n (A ∩ B)

n(A U B) = n(A) + n(B) - n (A ∩ B)

n(A U B)  = n(A - B)  + n (A ∩ B)  + n(B) + n (A ∩ B)   - n (A ∩ B)

=> n(A U B)  = 10 + 3 + 8 + 3 - 3

=>  n(A U B)  =  21

Shown in Venn Diagram in attached image

From the Venn Diagram

n(A U B)  = 10 + 8 + 3  = 21

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