Question

Please help with this multiple choice question for a finite course in college...

Let U={1,2,3,b,c,y,z} be a universal set with subsets Y={1,b,c,y}, X={c,y,z}, and A={1,2,c,z}. Another subset of U is given by S={z}. Which of the following sets are needed to express the set {S}? A. A B. Y C. X D. A' E. Y' F. X'

Answer 1

Any clues?

Answer 2

Is it S or {S} the question is looking for?

To express S={z}, we need more than one set.

Answer 3

Which set is needed to express the set S?

Answer 4

We have A, X, Y and the universal set U

Answer 5

those sets are above

Answer 6

hint:
Intersect X with a set which does not contain c and y, but contains z.
Can you find it?

Answer 7

I doubt it :)

Answer 8

It's on the answer list, look harder!!! :)

Answer 9

{Z}?

Answer 10

is it just choice A

Answer 11

Look at these one by one, and you'll find one which fits, i.e.
contains z, but no c, no y.
Note that notation ' is such that
A'=what's in U but not in A = {3,b,y}

Answer 12

Is it Y'?

Answer 13

A union (Y' intersect A') union (A' intersect Y') = {z}

Answer 14

So I'd say it' A' and Y' (assuming you mean that A' is the somplement of A etc)

Answer 15

complement*

Answer 16

Exactly!
So X intersect Y' will leave you with only z, which is S.

Answer 17

X={c,y,z}
Y={1,b,c,y}
Y'={2,3,z}
So X intersect Y'=z

Answer 18

I have tried to put in the choices for A' and Y' together and individually and they were not correct. Also this is a two part question but I can't view the other part until this is answered correctly.

Answer 19

mathmate is right, it's trivial! Ignore what I put, I forgot z was contained in Y'

Answer 20

This one has me stumped
i even tried X Y Y' for the answers and they were still wrong

Answer 21

Did you try
X intersect Y'=z
?

Answer 22

or
Y' intersect X
?