If A and B are two sets such that

Question:

If $A$ and $B$ are two sets such that $n(A)=24, n(B)=22$ and $n(A \cap B)=8$, find:

(i) $n(A \cup B)$

(ii) $n(A-B)$

(iii) $n(B-A)$

 

Solution:

Given:

$n(A)=24, n(B)=22$ and $n(A \cap B)=8$

To Find:

(i) $n(A \cup B)$

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

$=24+22-8$

$=38$

Therefore,

$n(A \cup B)=38$

(ii) $n(A-B)$

We know that,

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

$=24-8$

$=16$

Therefore,

$n(A-B)=16$

(iii) $n(B-A)$

We know that,

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

$=22-8$

$=14$

Therefore,

$n(B-A)=14$

 

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