Let U= q, r, s, t, u, v, w, x, y, z A = q, s, u, w, y B = q,...

Let U= {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} List the elements in the set resulting from the following operation: $A \cap B'$ a. {r, s, t, u, v, w, x, z} b. {t, v, x} c. {q, s, t, u, v, w, x, y} d. {u, w}

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Transcript

00:07 Okay, so we're given three different sets here in the universal set u.

00:13 We want to find the complement of b union a.

00:18 So we are going to start by finding just b union a.

00:23 Before we can find the complement, we have to know what set we're dealing with here.

00:26 A union of two sets like this means you're listing out every single element that appears in both of these sets.

00:32 So we're going to list all of a and then all of b.

00:35 However, in sets we never repeat elements.

00:38 So if there's something that is an element of a and an element of b, we're only going to write it once.

00:44 So what i'm going to do is i'm going to start by writing out all the elements of b, q, s, y, z.

00:51 And then i'm going to go list out all the elements of a.

00:55 But if it's something i've already written, i'm going to skip over it.

00:58 So, for example, i'm going to skip over the q, the s, and then i can write the u because it hasn't been written before.

01:03 I can also write the w, but i'm going to skip over the y because we already have that from b.

01:08 So this is our b union a.

01:10 Now to find b union a complement, what that means is it's any element that's in the universal set u that is not in this set we listed up above in green...

Question

Let U= {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z} List the elements in the set resulting from the following operation: $A \cap B'$ a. {r, s, t, u, v, w, x, z} b. {t, v, x} c. {q, s, t, u, v, w, x, y} d. {u, w}

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