Thread: Proving subsets =S

Hello
Iv got an exam in a week and am trying to get through my whole course in that week. And am off to a horrible start =/
Can someone please tell how i should go about proving questions like the follwoing.

Q1)

A = {x <element_of> R | cos x = 1}
A = {x <element_of> R | sin x = 0}
Show that A <subsest of> B


Q2)

X = {24k + 7 | k <element_of> Z}
Y = {4n + 3 | n <element_of> Z}
Z= {6m + 1 | m <element_of> Z}

prove: X <subset_of> Y and X <subset_of> Z but Y <not_subset_of> Z

Thanks and im sure alot more questions would be comming soon =(

Originally Posted by lost1

Hello
Iv got an exam in a week and am trying to get through my whole course in that week. And am off to a horrible start =/
Can someone please tell how i should go about proving questions like the follwoing.

Q1)

A = {x <element_of> R | cos x = 1}
A = {x <element_of> R | sin x = 0}
Show that A <subsest of> B


Q2)

X = {24k + 7 | k <element_of> Z}
Y = {4n + 3 | n <element_of> Z}
Z= {6m + 1 | m <element_of> Z}

prove: X <subset_of> Y and X <subset_of> Z but Y <not_subset_of> Z

Thanks and im sure alot more questions would be comming soon =(

Appeal to the definition of subset.

So for the first one. We want to show that if that .

Can you do that?

Hey thanks for the quick reply =)

hmm...yess i tried using the basic idea but couldnt get a proper proof. Would this be a clear enough proof:

Let x <element_of> A, that is cos x = 1
ie. x = 2kPi where k <element_of> N

Now, sin(x) = sin(2kPi) = 0 and therefor x <element_of> B
That is, A <subset_of> B

?

also, how do i show the maths symbols nicely like u have?

Originally Posted by lost1

Hey thanks for the quick reply =)

hmm...yess i tried using the basic idea but couldnt get a proper proof. Would this be a clear enough proof:

Let x <element_of> A, that is cos x = 1
ie. x = 2kPi where k <element_of> N

Now, sin(x) = sin(2kPi) = 0 and therefor x <element_of> B
That is, A <subset_of> B

?

Did you take a non-decript element of . Yes. Did you show that this element must be an element of . Yes. Did you give a complete and correct proof. Yes.

Originally Posted by lost1

also, how do i show the maths symbols nicely like u have?

Enclose them in math brackets For example. to do the you must merely enter

Code:

\underbrace{X\cup Y=\int_0^{\Phi}f_n(x)dx}_{\text{this}}

this enclosed in [ math] [/tex].

thanks =)
now how do i go about doing the second one?

Originally Posted by lost1

thanks =)
now how do i go about doing the second one?

Well And clearly .......so

ohh god i am thick arnt I...

Originally Posted by lost1

ohh god i am thick arnt I...

Nah. Little stupid things like that are always the hardest.

ok another quick question...

Prove if

and


then

My start at proof:
Let therefore

and then =/

also whats the code for intersection?