Question

Divide the integers between 1 and 100 into four sets: multiples of 2, multiples of 3, multiples of 5, and any remaining integers, then answer: a) How many integers in each set? b) How many integers in each possible intersection of two or more sets? c) How many integers in each set are exclusive to that set? Hint: use Venn diagram.

Answer 1

multipels av 2...2, 4, 6, 8, 10....100####number integers=(100/2)+1

multipels av 3...3, 6, 9, 12, 15....99##### number integers=round-down(100/3) +1...=34

multipels av 5...5, 10, 15, 20, 25...100#### number integers=(100/5)+1=21

Comments

There are four sets; how many in the fourth set (remaining integers not in the other sets)? The numbers in each set are overestimated: divide each set by 2, 3 or 5 as appropriate and you get 1, 2, 3 etc up to the last number, which tells you how many there are in the set: 50 (100=2*50); 33 (99=3*33); 20 (100=5*20). What are the answers to parts b) and c)?