Ques-Find-the-number-of-integers-in-the-set-S-1-2-3-60-which-are-not-divisible-by-2-nor-by-3-nor-by-5-Hello-

Question Number 193892 by Mastermind last updated on 22/Jun/23

Ques .

Find the number of integers in the set

S = {1, 2, 3, \dots, 60} which are not divisible

by 2 nor by 3 nor by 5 .

Hello

Answered by BaliramKumar last updated on 22/Jun/23

60 \times \frac{2 - 1}{2} \times \frac{3 - 1}{3} \times \frac{5 - 1}{5}

60 \times \frac{1}{2} \times \frac{2}{3} \times \frac{4}{5} = 16

Commented by SaRahAli last updated on 22/Jun/23

?

Commented by Mastermind last updated on 22/Jun/23

Than you so much

Answered by MM42 last updated on 22/Jun/23

l e t A, B, C \subset S & A : 2 k; B : 3 k; C : 5 k

∣ A ∣= 30 & ∣ B ∣= 20 & ∣ C ∣= 12

∣ A \cap B ∣= 10 & ∣ A \cap C ∣= 6 & ∣ B \cap C ∣= 4 & ∣ A \cap B \cap C ∣= 2

∣ A \cup B \cup C ∣= 30 + 20 + 12 - 10 - 6 - 4 + 2 = 44

a n s = 60 - 44 = 16

Commented by Mastermind last updated on 22/Jun/23

Thank you