00:01
Okay, the question is, are these sets equivalent? we've got set j, which is the set of all x, such that x equals 3n plus 3, and n is a member of the set of whole numbers.
00:17
And then l is x, such that x is 3n minus 3, where n is a member of the set of natural numbers.
00:29
So let's start writing these out in list form, then compare them.
00:37
So my expression is 3n plus 3, n's got to be a whole number.
00:43
Let's start with the lowest whole number, so that's 0.
00:51
So our first member, our lowest member of the set is 3 times 0 plus 3.
00:58
Then we can look at 3 times 1 plus 3, 3 times 2 plus 3, etc.
01:08
So let's simplify that.
01:11
3 times 0 plus 3 is 3, 3 times 1 plus 3 is 6, 3 times 2 plus 3 is 9, and you can see we'll just be counting by 3s from there on out.
01:27
Okay, so that's what j looks like as a list.
01:33
How about l? l, our expression is 3n minus 3, n's got to be a natural number.
01:42
The lowest natural number is 1.
01:45
So let's plug in 1, and then we'll go to 2, and then we'll go to 3, etc...