Question

if a and b are two sets such that n(A)=240n(B) =350 and n(AUB)=500 find n(ANB)
please help​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

• n(A) = 240
• n(B) = 350
• n(AUB) = 500

${\bf{\blue{\underline{To\:Find:}}}}$

• n(AnB) =?

${\bf{\blue{\underline{Formula\:Used:}}}}$

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

${\bf{\blue{\underline{Now:}}}}$

$: \implies{\sf{ 500 = 240 + 350 - n(A \cap \: B)}}$

$: \implies{\sf{ 500 = 590 - n(A \cap \: B)}}$

$: \implies{\sf{ 500 -590= - n(A \cap \: B)}}$

$: \implies{\sf{-90= - n(A \cap \: B)}}$

$: \implies{\sf{ n(A \cap \: B)=90}}$