Question

Determine the following. A ∪ (B ∩ C)

Answer 1

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}.

Answer 2

Hey ace!
let's start with the parentheses first,

(B ∩ C) = {q, s, y, z} ∩ {v, w, x, y, z}.

Intersection will be the elements which appear in BOTH sets.
So which letters does that give us?

Answer 3

Ooo it's not copy/pasting correctly... sec..

Answer 4

\[\Large\rm (B \cap C) = \{q, s, y, z\} \cap \{v, w, x, y, z\}\]

Answer 5

umm q,s,v,w,x,y,z?

Answer 6

No no no, you're thinking union.\[\Large\rm (B \cap C) = \{q, s, \color{orangered}{y, z}\} \cap \{v, w, x, \color{orangered}{y, z}\}\]The orange ones are the only ones showing up in BOTH sets, yes?

Answer 7

ohh ok yes they are.

Answer 8

\[\Large\rm (B\cap C)=\{y,z\}\]
So that gets us to this point,\[\Large\rm A\cup (B\cap C)\quad=\quad A\cup \{y,z\}\]

Answer 9

So now we need to figure this out:\[\Large\rm \{q, s, u, w, y\}\cup \{y,z\}\]

Answer 10

this would be q,s,u ? or is it just y

Answer 11

Remember what you were trying to do with B and C earlier?
That's what we want to do here.

We want ALLLLLL of the stuff.
That's what the union is.

he's a friendly operator, he's like "Let's just all hang out. I don't care what color your skin is, what you look like, woah woah come on shelly, I know you've had some troubles in the past .. but forget about that here, everyone is accepted."

Answer 12

So we want all of the stuff.
Just remember that you shouldn't have repeat elements!
So when we do our union, we won't end up with y, y in our set.
We'll just have one y element.

Answer 13

\[\Large\rm \{q, s, u, w, y\}\cup \{y,z\}\quad=\quad\{q,s,u,w,y,z\}\]Something like that, yes? Good?

Answer 14

ohh ok I'm understanding a little better now~

Answer 15

I know I know I know... Can be tough getting used to these weird math symbols.
Throw up a few more questions on the site, you'll get it soon enough :3

Answer 16

lol ok thanks a lot~