00:01
We have set s, the set of all strings of zeros and ones of length 4, and we have two subsets of s.
00:11
Subset a has four elements.
00:15
They are the strings of zeros and ones, 1 -0 -11, 11 -1 -1 -0 -1 -0, and 0 -1 -0.
00:27
And b is the set of the strings 1 -0 -0 -0 -0 -1 -0 -1 -0 -1 -0 -1 -0.
00:38
We want to find each of the following operation on the sets a and b, knowing that the universe is the set s of all strings of 0 -1s of length 4, we want to find then a intersection v, a union b, a minus b, and b minus a.
00:59
So let's start with part a, a intersection b, that is the elements that are at the same time in a and b.
01:08
And which are these elements? well, we see 0 -110 is one of those elements.
01:17
Let's see there is another 0 -0 -1 -1.
01:21
It's not there.
01:24
Not there and one triple zero is not there.
01:29
So the only element in both a and b is the string 0 -110.
01:37
That's the intersection of a and b.
01:41
Now in part b we find the union of a and b and that consists of all elements in a or in b.
01:52
Or better said in a or b.
01:55
That is we put all elements we found in both sets inside this new set here and of course we don't repeat the elements when they are in common in a and b in this case we know is the only one that is repeated in both sets is 0 -110 because it's the intersection we found in part a so we're going to put all strings and this one here 0 -110 we put it once so we get 1 -0 -1 -1 -0 -0 -1 -0 we put it once so we get 1 -0 -0 -1 -0 0111, 0100, 0110, 111 have put all elements in a, now in b, without repeating 0111, so we put these only these three elements...