Answer :
Answer:100
Step-by-step explanation:
Suppose S is the set of number of first 300 natural number
[tex]S=\{1,2,3,4.......300\}[/tex]
And A be the set of number divisible by 2
[tex]A=\{2,4,6.......300\}[/tex]
so total element in A is [tex]\frac{300}{2}=150[/tex]
Let B be the set containing the element divisible by 3
[tex]B=\{3,6,9......300\}[/tex]
So element in B is [tex]\frac{300}{3}=100[/tex]
But there are some element which is common in both A and B
so [tex]A\cap B={6,12,18.......300}[/tex]
Element in [tex]A\cap B=\frac{300}{6}=50[/tex]
and so number of elements which are less than 300 and neither divisible by 2 nor 3 is
[tex]=n(S)-n(A\cup B)[/tex]
[tex]=300-(n(A)+n(B)-n(A\cap B))[/tex]
[tex]=300-(150+100-50)[/tex]
[tex]=300-200[/tex]
[tex]=100[/tex]