Question

find n(a ∩ b) if n(A)=16,n(B)=14 and n(a union b)=25​

Answer 1

Answer:

5

Step-by-step explanation:

n(a intersection b)=n(a)+n(b)-n(a union b)

n(a intersection b)= 16+14-25

5

Answer 2

$\maltese$ Given :-

$n(A) = 16 \\n(B) = 14 \\n (A\cup B)= 25$

$\maltese$ To find :-

$n (A \cap B)$

$\maltese$ SOLUTION :-

We have formula that is

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

On substituting the values we get ,

$25 = 16+14 - n(A\cap B)$

$25 = 30 - n(A \cap B)$

$25-30 = -n(A\cap B)$

$-5= -n (A \cap B )$

$n (A \cap B ) = 5$

$\maltese$ Know more formulae:-

If A,B are two disjoint sets ,

$n (A\cup B) = n (A) +n(B)$

$n (A-B) +n (A\cap B) = n(A)$

$n (B-A) + n (A\cap B) = n (B)$

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