Question

if n (A) = 7,n (b)=13,n(a ^B) = 4 then n (AUB)=?



PLZ ANS WITH FORMULA PLZ ​

Answer 1

$\bf{\underline{\underline{Question-}}}$

if n (ɑ) = 7,n (b)=13,n(A∩B) = 4 then n (ɑUB)=?

ㅤ

$\bf{\underline{\underline{Answer-}}}$

ㅤ

$\bf\fbox\green{Given-}$

ㅤ ㅤㅤㅤ ㅤㅤn(A) = 7

ㅤ ㅤㅤㅤ ㅤㅤn(B) = 13

ㅤ ㅤㅤㅤ ㅤㅤn(A∩B) = 4

ㅤ ㅤㅤㅤ ㅤㅤ

$\bf\fbox\purple{To \: Find-}$

ㅤ ㅤㅤㅤ ㅤn(A∪B) = ?

ㅤ ㅤㅤㅤ

ㅤ ㅤㅤㅤ

$\bf{\underline{\underline{Solution-}}}$

Since, ㅤn(A∪B) = n(A) + n(B) - n(A∩B)

ㅤ ㅤㅤㅤn(A∪B) = 7 + 13 - 4

ㅤ ㅤ ㅤn(A∪B) = 16.

$\bf\fbox\red{↦ \: n(A∪B) = 16}$

ㅤ ㅤㅤㅤ ㅤ

ㅤ ㅤㅤㅤ ㅤ

ㅤ ㅤㅤㅤ ㅤ

$\bf{\underline{\underline{Formula}}}$

ㅤ ㅤㅤㅤ ㅤ

The formulɑ for the number of elements in ɑ union B is n(ɑ U B) = n(ɑ) + n(B) - n(ɑ ∩ B).