Question

If N = {all real numbers} and subset S = {multiples of 4 less than zero}, what is S′?

{multiples of 4 greater than zero}

{even numbers less than zero}

{odd numbers less than zero}

{all real numbers excluding multiples of 4 less than zero}

Answer 1

S' = N\S?

Answer 2

@shahbaaz786

\(\bf S'\) is the complement of \(\bf S \) then \(\bf S'\) contains all elements which S doesn't contain. Hence:\[\bf \left\{ S \subset N \ | N = \mathbb{R}, \ S=4k<0 \ for \ k < 0 \right\} \implies S' = N-S=N / S\]
@zzr0ck3r is right. Note that my "/" should really be "\" to denote a relative set but the equation editor doesn't allow me to do that for some reason...

Answer 3

Isn't S' the complement of S?

Answer 4

it is, and here s is a subset of universe N = R
so
R\S
remove S from R

Answer 5

So therefore, it would be all elements of R that are not contained in S.

Answer 6

yup, that's right.

Answer 7

Which is, all real numbers that are not multiples of 4 less than 0.
Does that make sense?

Answer 8

its important to state the universe of shich S is being complimented with

Answer 9

Z\S and R\S are two different things

Answer 10

True...

Answer 11

IOW S' depends on the universe S is a subset of

Answer 12

so its D ?

Answer 13

two very different things..

Answer 14

Well, if it were Z then instead of real numbers it would be integers, et cetera.
Yes I think it is D.

Answer 15

@shahbaaz786 correct.

Answer 16

correct

Answer 17

its trivial, but we need to know that S was in N=R

Answer 18

@zzr0ck3r we already know that...

Answer 19

p.s. your book is lame for calling R = N

Answer 20

and i agree lol since the N can easily be confused with the natural numbers... @zzr0ck3r