Question

n(a) =12, n(B)=15 then n(A union B)=25 then find n(A intersection B)=?
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Answer 1

AnSwEr

${\tt{\red{\underline{\large{Given}}}}}$

• $\sf{n(a)=12\:And{n(B)}=15}$
• $\sf{n(a)\cup{n(B)}}=25$

${\sf{\green{\underline{\large{To\:find}}}}}$

• $\sf{n(a)\cap{n(B)}}$

${\sf{\pink{\underline{\Large{Explanation}}}}}$

Formula

$\sf{n(a)\cap{n(B)}}={n(a)+n(B)-}{n(a)\cup{n(B)}}$

putting values

$\implies\sf{n(a)\cap{n(B)}}={n(a)+n(B)-}{n(a)\cup{n(B)}}$

$\implies\sf{n(a)\cap{n(B)}}={12+15-}{n(a)\cup{n(B)}}$

$\implies\sf{n(a)\cap{n(B)}}={27-}25$

$\therefore\sf{n(a)\cap{n(B)}}=2$

Hence value of $\therefore\sf{n(a)\cap{n(B)}}=2$