Question

$\textbf{How many natural numbers upto 2001}\\\textbf{are divisible by 3 or 4 but NOT by 5 ?} \\ \\ \sf \: full \: solution \: plzzz. \: no \: spam.$
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Answer 1

||✪✪ QUESTION ✪✪||

• How Many Natural Numbers upto 2001 are Divisible by 3 or 4 but Not by 5 ?

|| ✰✰ ANSWER ✰✰ ||

➻ Total Number upto 2001 That are divisible by 3 = n(3) = (2001/3) = 667

➻ Total Number upto 2001 That are divisible by 4 = n(4) = (2001/4) = 500

➻ Total Number upto 2001 That are divisible by 12 = n(3∩4) = (2001/12) = 166

➻ Total Number upto 2001 That are divisible by 15 = n(3∩5) = (2001/15) = 133

➻ Total Number upto 2001 That are divisible by 20 = n(4∩5) = (2001/20) = 100

➻ Total Number upto 2001 That are divisible by 60 = n(3∩4∩5)= (2001/60) = 33

_____________________________

Now , we Know That :-

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(A∩C) - n(B∩C) + n(A∩B∩C)

Putting Values we get :-

☛ 667 + 500 - 166 - 133 - 100 + 33

☛ 1200 - 399

☛ 801 (Ans).

Hence, Their are Total 801 Natural Numbers upto 2001 which are divisible by 3 or 4 but NOT by 5 ..

Answer 2

Refer The Attachment.........