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}

Determine the following.
(B' ∩ C)' ∪ A

Answer 1

First you need to find the set B'

How do we do this?

Answer 2

any ideas?

Answer 3

By drawing a diagram?

Answer 4

you could do it that way, but it might get a bit messy

Answer 5

Here's what I had in mind

Answer 6

you start with set U = {q, r, s, t, u, v, w, x, y, z}

then you erase the elements that you find in set B. So erase q, s, u, w, y and you'll be left with the set B'

B' = {r, t, v, x, z}

Answer 7

now what elements are in both

C = {v, w, x, y, z}

AND

B' = {r, t, v, x, z}

Answer 8

v, x,z

Answer 9

So

B' ∩ C = {v,x,z}

Answer 10

Now to find (B' ∩ C)' we start with set U again, and kick out the elements v, x, z (since they are in B' ∩ C)

This gives us

(B' ∩ C)' = {q, r, s, t, u, w, y}

Answer 11

now just union that with set A and you are done

Answer 12

{q, r, s, t, u, w, y, z} ?

Answer 13

one sec, correcting a typo

Answer 14

This problem I'm trying to solve is multiple choice and some of the answers are
A. {q, s, u, v, w, x, y}

B. {q, s, u, y}

C. {q, r, s, t, u, w, y, z}

D. {q, r, s, t, u, v, w, x, y}

And I chose C

Answer 15

oh wait...i made a typo at the top...let me do everything over and put it all in one place



Step 1)


Find B'


Start with U = {q, r, s, t, u, v, w, x, y, z} and erase q,s,y,z


B' = {r, t, u, v, w, x}
C = {v, w, x, y, z}

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Step 2)

Intersect set B' with set C to get


B' ∩ C = {v, w, x}


This is the set of elements that are in BOTH sets B' AND C


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Step 4)

Start with set U again and kick out elements v, w, x


{q, r, s, t, u, y, z}


-------------------------------------------------------

Step 5)


Now union this with set A


{q, r, s, t, u, y, z} U {q, s, u, w, y}


{q, r, s, t, u, w, y, z}


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So the answer is

{q, r, s, t, u, w, y, z}


So you are absolutely correct, it's C

Answer 16

Thanks!

Answer 17

you're welcome