Problem discrete math

Question

Let A = {1, 2, . . . , 999}. (a) Find how many numbers in A are not divisible by 3 and 7.

(b) Find the number of subsets B ⊆ A such that B ∩ {1, 2, 3, 4} = {1, 2}.

Answer 1

999/3=333 are divisible by 3

3,6,9,12,15,...333, 336,339, ...993,996,999

999/7=142 5/7

7,14,21,...,147,154, ...994

999/21=47 12/21, 47 divisible by 3 and 7

333+142= 475

475-47= 428 total divisible by 3 or 7

999-428= 571 not divisible by 3 or 7