00:01
Hi, here we are given that we have three sets, a, b, sorry, four sets, a, b, c and d.
00:09
A is a subset of b.
00:11
C is a proper subset of d.
00:13
That means c is not equal to d.
00:15
And given these two assumptions, we want to show these two inclusions that a union c is a subset of b union d and that a intersection c is a subset of b intersection d.
00:29
So let's start with the first one.
00:33
First, so we want to show, so this is what we want to show first.
00:38
So what we are going to do and let's just give some names on the assumptions.
00:44
Let's just call this assumption a1, although we might not even need this, and let's call this assumption a2.
00:55
Okay, so now, to show we saw that one set is a subset of another, we take an element in the set that we think it's smaller and we show that it is also an element in of the set that we think is bigger...