Find (a)QnR(b)P^1nR^1 (c) (PnQ)^1

[Chikis]

The universal set is the set of all interger and the subsets P,Q,R of are given by
[math]P=\{x : \le0\}[/math]
[math]Q=\{....,-5,-3,-1, 1, 3, 5....\}[/math]
[math]R=\{x: -2\le x<7\}[/math]
Find:
[math](a)Q\cap{R}[/math]
[math](b)P'\cap{R'}[/math]
[math](c )(P\cap{Q)'}[/math]

I need guidance in tackling this problem.

Moderator please help me remove the other two redundant threads.

Edited August 20, 2014 by imatfaal
fixing latex

[CaptainPanic]

!

Moderator Note

Homework Help Rules

A simple reminder to all: this is the "Homework Help" forum, not the "Homework Answers" forum. We will not do your work for you, only point you in the right direction. Posts that do give the answers may be removed.

So Chikis would you explain where you have got to in solving this problem and what has stopped your progress - hopefully members can then help you to overcome your difficulties yourself.

[studiot]

I suggest you draw a diagram shown the regions for each set involved.

 

What do you notice?

[imatfaal]

Chikis - I fixed your latex. Hope I got the expression right! The problem was (c) I think it recognizes this as shortcode for the copyright symbol © - but doesnt have the copyright symbol installed and just says syntax error

[Chikis]

Chikis - I fixed your latex. Hope I got the expression right!

Yes. You got it.

[studiot]

So how about your diagram as suggested?

[Chikis]

My first problem concerning this problem:

Do these mean the same thing?

 

1[math]P'\cap R'[/math]and[math](P\cap R)'[/math]

 

 

2[math]( P\cap Q)'[/math]and[math]P'\cap Q'[/math]

Edited August 21, 2014 by Chikis

[imatfaal]

My first problem concerning this problem:

Do these mean the same thing?

 

1[math]P'\cap R'[/math]and[math](P\cap R)'[/math]

 

 

2[math]( P\cap Q)'[/math]and[math]P'\cap Q'[/math]

 

I never learnt sets formally - so my approach is very home spun.

 

Firstly do you think those terms above mean the same in general? A little thought will give you an answer to this - or try with a few made up sets and actually enumerate.

 

Secondly, you really should make a diagram. With a few minutes you can easily display everything and get a grip where things go.

 

Thirdly, I would rephrase/rewrite the question so that you understand what the sets really entail. R is limited in size, P and Q are not but both can still be described/thought of with a few words. I would rewrite so that all three are in same format.

 

Fourthly, try to understand what P' n R' and (PnQ)' actually mean - ie everything which is outside P and at the same time outside R, everything which is not in both P and Q.

 

Chikis - getting your latex correct is laudable, but understanding what the problem means is so much more important.

[Chikis]

Fourthly, try to understand what P' n R' and (PnQ)' actually mean - ie everything which is outside P and at the same time outside R, everything which is not in both P and Q.

So say for example does P' mean opposite or reverse of all the element in set P?

Let me see if I can interprete what

[math]P=\{x : \le0\}[/math]and[math]R=\{x: -2\le x<7\}[/math] mean respectively.

Could [math]P=\{x : \le0\}[/math] mean

[math]P=\{....-3,-2,-1,0\} [/math]

and [math]R=\{x: -2\le x<7\}[/math] mean[math]\{-2,-1,0,1,2,3,4,5,6\}[/math]?

Edited August 24, 2014 by Chikis

[imatfaal]

Can you now draw a diagram?

 

If not run through this page https://www.khanacademy.org/math/probability/independent-dependent-probability/basic_set_operations/v/universal-set-and-absolute-complement

 

and perhaps the others in that unit.

[Chikis]

Must I draw a the diagram to solve this problem? I feel that is not necessary. I just need to understand this problem.

[studiot]

 

chikis

 

Must I draw a the diagram to solve this problem? I feel that is not necessary. I just need to understand this problem.

 

 

Most people find a diagram helpful which is why one has bee suggested.

 

If you wish to struggle on without one then let us work through your problem using the alternative method imatfaal offered

 

imatfaal

 

Thirdly, I would rephrase/rewrite the question so that you understand what the sets really entail. R is limited in size, P and Q are not but both can still be described/thought of with a few words.

 

Starting at the first part

 

What do you think the statement Q intersection R means in words?

 

Never mind the negation or complementation in the other questions for the moment they are only a distraction to the first part.

Edited August 29, 2014 by studiot

[Chikis]

[math]P=\{...,-3,-2,-1,0\}[/math][math]Q=\{...,-5,-3,-1,1,3,5,...\}[/math][math]R=\{-2,-1,0,1,2,...,6\}[/math]based on the above subsets[math]U=\{...,-2,-1,0,1,2,...,7,9,11,13,....\}[/math]

[math]\therefore[/math][math]Q\cap R=\{-1,1,3,5\}[/math]

[math]P'=\{1,2,...6,7,9,11,...\}[/math]

[math]R'=\{...,-5,-4,-3,7,9,11,13,...\}[/math][math]P'\cap R'=\{7,9,11,13,...\}[/math]

[math]P\cap Q=\{...,-7,-5,-3,-1\}[/math][math](P \cap Q)'=\{...,-8,-6,-4,-2,0,1,2,3,...,7,9,11,...\}[/math]

Edited September 3, 2014 by Chikis

[imatfaal]

The universal set is the set of all interger and the subsets P,Q,R of are given by

 

 

[math]U=\{...,-2,-1,0,1,2,...,7,9,11,13,....\}[/math]

 

You need to be consistent

One of the above is clearly wrong.

 

Have a read here - http://www.mathsisfun.com/sets/venn-diagrams.html

[studiot]

 

based on the above subsets

 

You have gone against what I asked and again gone wrong.

 

What I asked was designed specifically to help.

 

 

What do you think the statement Q intersection R means in words?

[Chikis]

 

 

You need to be consistent

 

One of the above is clearly wrong.

 

Have a read here - http://www.mathsisfun.com/sets/venn-diagrams.html

What is wrong here? The whole thing seems right to me. Could you help me figure out what is wrong?

[studiot]

 

What is wrong here? The whole thing seems right to me. Could you help me figure out what is wrong?

 

 

Why should I, when you won't cooperate with what I have to say?

 

Your error is in the quote, look again at your first post.

[Chikis]

[math]U=\{...,-2,-1,0,1,2,...,7,9,11,13,....\}[/math]

Am thinking that all the subsets are contained in the universal set. I can hardly figure what is wrong what in the universal set. Please help me. I have really suffered on this.

[studiot]

 

I have really suffered on this.

 

 

Well have you even attempted what I asked?

 

It was a very simple request.

 

 

Studiot

What do you think the statement Q intersection R means in words?

 

Yet your response was to introduce a universal set, that was not correct, and not called for by that part of the question.

 

P, Q and R are all sets of numbers.

 

But they are not sets of the same types of number.

 

In particular, as you have written them in Post#1, P and R are sets of real numbers

Q is a set of integers.

 

Back to my question

 

The intersection of Q with R refers to a set that contains only numbers that are in both Q and R.

 

Q contains all the odd integers, excluding 0, which is neither odd nor even.

 

R contains a restricted interval of real numbers, which includes all the integers in that interval.

 

So the intersection of Q with R boils down to all the integers, excluding 0, that are in the interval containing R.

 

That is what I mean by stating in words.

 

Can you now state this in symbols?

Edited September 4, 2014 by studiot

[John]

All the sets seemingly are supposed to be subsets of the integers.

 

This is what I take from the opening line,

 

The universal set is the set of all interger and the subsets P,Q,R of are given by

 

anyway.

Edited September 4, 2014 by John

[studiot]

Thank you John, that would make the problem easier.

 

So that would make this first part you did correct.

 

based on the above subsets

[Chikis]

 

Yet your response was to introduce a universal set, that was not correct, and not called for by that part of the question.

Did I do wrong to introduce the universal set?

 

But they are not sets of the same types of number.

Universal set may contain diffrent number which are elements of different subsets.

 

Q contains all the odd integers, excluding 0, which is neither odd nor even.

Are you saying that zero is not an even numbers? I believe these are lists of even numbers : 0, 2, 4, 6, 8, 10, ...,

 

 

Can you now state this in symbols?

Let me try to be specific now. I can find

 

[math](b)P\cap{R}[/math]

[math](c )(P\cap{Q}[/math] without introducing a universal set. My main problem is how to find

[math](b)P'\cap{R'}[/math]

[math](c )(P\cap{Q)'}[/math]

I had that problem because of the compliment involved and there is no universal set introduced. So I had to introduce one if I must tackle the problem.