Question

if n(a) =400 , n(b)= 200 , n(anb) = 50 . find n(aub )​

Answer 1

Answer:

Ans. (c).n(A∩B)=n(A∪B)

=n(u)−n(A∪B)

=n(u)−{n(A)+n(B)−n(A∩B)}

=700−{200+300−100}=300

Answer 2

$\green{\large\underline{\sf{Given- }}}$

$\rm :\longmapsto\:n(A) = 400$

$\rm :\longmapsto\:n(B) = 200$

$\rm :\longmapsto\:n(A\cap B) = 50$

$\purple{\large\underline{\sf{To\:Find - }}}$

$\rm :\longmapsto\:n(A\cup B)$

$\pink{\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}}$

$\boxed{\tt{ \: n(A\cup B) = n(A) + n(B) - n(A\cap B) \: }}$

$\red{\large\underline{\sf{Solution-}}}$

Given that,

$\rm :\longmapsto\:n(A) = 400$

$\rm :\longmapsto\:n(B) = 200$

$\rm :\longmapsto\:n(A\cap B) = 50$

So, using the formula

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

$\rm :\longmapsto\:n(A\cup B) = 400 + 200 - 50$

$\rm :\longmapsto\:n(A\cup B) = 600 - 50$

$\rm\implies \: \: \: \boxed{\tt{ \: \: n(A\cup B) \: \: = \: \: 650 \: \: }}$

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Additional Information

$\boxed{\tt{ n(A - B) = n(A) - n(A\cap B) \: }}$

$\boxed{\tt{ n(B - A) = n(B) - n(A\cap B) \: }}$

$\boxed{\tt{ n(A\cup B) = n(A - B) + n(A\cap B) + n(B - A)}}$

De Morgan's Law

$\boxed{\tt{ \: (A\cup B)' = A'\cap B' \: }}$

$\boxed{\tt{ \: (A\cap B)' = A'\cup B' \: }}$