Question

Consider a set of integers from 12 to 50 find how many numbers are divisible by 3 or 7 or 5 also indicate how

Answer 1

Answer:

Step-by-step explanation:

I will give certain hints to your problem. I will leave it to you to figure out the answer for yourself. Let A3A3, A5A5, and A7A7 denote the set of numbers from 11 to 500500 which are divisible by 33, 55 and 77, respectively. Let |A3||A3|, |A5||A5| and |A7||A7| denote the number of elements of A3A3, A5A5 and A7A7, respectively.

Hint 11: The set of numbers, from 11 to 500500, which are divisible by at least one of 33, 55 and 77 is A3∪A5∪A7A3∪A5∪A7.

Hint 22: The set of numbers, from 11 to 500500, which are divisible by both ii and jj, for i,j∈{3,5,7}i,j∈{3,5,7}, is Ai∩AjAi∩Aj. Similarly, the set of numbers divisible by all of 33, 55 and 77 is A3∩A5∩A7A3∩A5∩A7.

Hint 33: By the principle of inclusion-exclusion,

||A3∪A5∪A7|=|A3|+|A5|+|A7|−|A3∩A5|−|A3∩A7|−|A5∩A7|+|A3∩A5∩A7||A3∪A5∪A7|=|A3|+|A5|+|A7|−|A3∩A5|−|A3∩A7|−|A5∩A7|+|A3∩A5∩A7| .

I think the above hints are very much sufficient to solve your problem.