00:01
Let a be the integers that are divisible by 2.
00:03
Let b be the integers that are divisible by 3.
00:07
And let c be the integers that are divisible by 5.
00:10
Right? so now, we have been given a set which has numbers from 1 to 100.
00:16
Right? so see, by the inclusion -exclusion principle, we will have the formula that this would be a union b union c is equals to, this would be a plus b plus c minus, you'll have a intersection b minus, this would be a intersection c and then minus, you'll have b intersection c and then plus a intersection b intersection c.
00:47
Right? we have this.
00:48
So see, over here, a union b union c, this is representing all those numbers that are multiple of 2, 3 and 5.
00:55
And we have a intersection b.
00:59
They are representing all the numbers that are divisible by 2 and 3.
01:03
That is the multiple of 6.
01:04
So you'll have over here, this is equals to 6, 12, 18 and so on till 96.
01:11
So there are total of 16 such numbers.
01:14
Then we have over here, a intersection c.
01:16
That is, these are the numbers which are divisible by 2 and 5.
01:20
That is the multiple of 10.
01:21
So you will have 10, 20, 30.
01:24
So on till 100.
01:26
And there are 10 such numbers.
01:28
Then we have b intersection c.
01:31
So these are the numbers which are divisible by 3 and 5.
01:35
That is the multiple of 15.
01:37
So such numbers are over here, 15, 30, 45 and so on till over here, you'll have 90...