If A and B are two sets such than

Question:

If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B).

Hint $n(B)=n(B-A)+n(A \cap B) \Rightarrow n(A \cap B)=(39-13)=26$

 

 

Solution:

 Given: n(A) = 54, n(B) = 39, n(B – A) = 13

Using the hint

$n(B)=n(B-A)+n(A \cap B)$

$\Rightarrow 39=13+n(A \cap B)$

$\Rightarrow n(A \cap B)=39-13$

$\Rightarrow n(A \cap B)=26$

Visualizing the hint given

We know that $n(A \cup B)=n(A)+n(B)-n(A \cap B)$

$\Rightarrow \mathrm{n}(\mathrm{A} \cup \mathrm{B})=54+39-26$

$\Rightarrow \mathrm{n}(\mathrm{A} \cup \mathrm{B})=67$

Hence $n(A \cup B)=67$

 

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