00:00So, in this question we are given,
00:01set contains the first 250 natural numbers.
00:05There are multiples of 3
00:06and set contains the first 201 natural numbers.
00:11So, set is 3, 6, 9, 12, 15.
00:16If we consider, 0 is also a multiple of 3.
00:19So, why is it not in this set?
00:22Because it is a whole number, not natural.
00:24So, first natural number multiple is 3.
00:27In the same way, here also natural numbers are given
00:32and even numbers.
00:33So, it will be 2, 4, 6, 8, and 12 and so on.
00:37And how many elements it have?
00:39It have 200 and set have 250.
00:44We are asked how many elements a union we have.
00:48So, we will add the number of elements in a
00:51plus number of elements in b
00:54minus number of elements in a intersection b.
00:59Why?
01:00Because 6 is in a also and b also.
01:04So, in a union b, it will be just one time.
01:07But here it will be counted one time in this, one time in this.
01:10So, 6 will be counted two times.
01:12So, we will subtract it one times.
01:15So, the elements which are common will be subtracted.
01:19Number of elements which are common.
01:21So, let's find out how many number of elements are common.
01:25So, we can see, here 3 into 2, 6 and here 6 is on third number.
01:33So, we can see, the element which is on second position is equal to its 3n position.
01:40Which are common.
01:42So, its fourth element will be same as its, put the value of n, keep increasing.
01:49Will be equal to its, here 6th element, which means here 12.
01:57So, first of all, we will find out which will be the limit part.
02:01So, we know this number is smaller and multiple is also 3n.
02:06So, we have to find 3n is equal to 200.
02:11And n is equal to 200 divided by 3.
02:17n is equal to 3, 6, 18 and divide 200 by 3.
02:263, 6, 18, 20.
02:2936, 16, 66 point something.
02:33But, the half element will not come.
02:36So, there will be 66 elements in this set.
02:39Which will be in this set also.
02:42In this set, it will go till number 132.
02:47So, 66 elements are common in both sets.
02:50So, we will write 200 plus 250 minus 66 is equal to A union B.
02:58Which will be 450 minus 66.
03:01Which will be 400 minus 16.
03:09Which will be 384.
03:13So, that will be the final answer.
03:16So, that will be the final answer.
03:16Go, go, go!
