Question

if n(A) = 45, n (B) = 60 and n(AUB) = 100 then n(A intersection B) is​

Answer 1

$\rm \bigstar \underline{Note}$

(A intersection B) is written as A∩B and symbol used to denote the intersection of sets A and B is ∩

$\rm \bigstar \underline{Given \: that }$

• n(A) = 45n

• n(B) = 60

• n(AUB) = 100

$\rm \bigstar \underline{To \: Find }$

• n(A∩B)

$\rm \bigstar \underline{Formula \: used }$

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

$\rm \bigstar \underline{Calculation}$

• Put the given values in this formula and solve

$\rm \mapsto \:100= 45+60 \: - \: n ( A \cap B )$

$\rm \mapsto \:100= 105 \: - \: n ( A \cap B )$

$\rm \implies \: n ( A \cap B ) = 105 - 100$

$\rm \implies \: n ( A \cap B ) = 5$

$\rm \bigstar \underline{Therefore}$

$\bf\implies \: n ( A \cap B ) = \boxed{ 5}$

$\\ {\underline{\rule{300pt}{9pt}}}$

$\rm \bigstar \underline{Verfication}$

$\rm \mapsto \:100= 45+60 \: - \: ( 5)$

$\rm \mapsto \:100= 105 \: - (5)$

$\rm \mapsto \:100= 100$

$\rm \mapsto \: L.H.S = R.H.S$

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

Answer:

$\huge\red{Answer}$

we have formula,

n(A∪ B)= n(U)− n(A∪ B)

′

n(A∪ B)= 60− 10= 50

Now,

n(A∪ B)= n(A)+ n(B)− n(A∩ B)

50= 35+ 24− n(A∩ B)

∴ n(A∩ B)= 9