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Any person who professional in math specially in (sets)plz enter and try solve this

fahdaldapy2002

Posted: Submitted by fahdaldapy2002 on 12 June 2008 - 5:39pm.

Joined: 2008-06-12
Posts: 24

Given that U = {x : x is real numbers}, A = {x : x is positive integer}, B = {x : x is negative integers},
C = {x : x = a/b, where a and b are integers with b not equal to 0}. Draw separate Venn diagrams for each of the following sets, shading those areas that represent the set.

(a) M = {1, 3, 5 ,7 ,9 …..}

(b) P = {x : x2 = 2}

© Q = {x : (2 – x) > 3, x is integers}

(d) R = {x : 2x = 0}

(e) T = {x : x = 2πr, r is a positive integers, π is Pi}

Colin

Posted: 13 June 2008 - 10:03am

Joined: 2007-10-17
Posts: 109

Well, I'm not sure if I could be called professional, but I'll have a go (I use the empty set symbol as my little image because I like the symbol, I'm not trying to say what sort of maths I'm into). Perhaps the reason no one's responded yet is that Venn diagrams might be tricky on the forums. I'll have to try to describe them.

Presumably U stands for universe of discourse. In which case draw a big square each time to represent U and always draw everything else inside it. For C you should draw a big circle inside the square and, since every integer is also a rational number, for A and B you should draw two smaller circles inside the circle representing C. Those circles shouldn't overlap, as there are no integers which are both positive and negative.

It's a little tricky to guess what they're asking of you now. As a guess, since everything in M is a positive integer, you're meant to draw a little circle inside A and shade that in. For P, I'm not entirely sure what you mean, but I think you mean $x^2$ (it's handy when you know how to do that, but it does take a while to pick it up). If that's right, then you'll see that the numbers for which that works are 2 and -2. You should probably shade in two little dots, one in A and one in B, for those two numbers.

You've got to love the computer's rendering of your typing for the next question. As for Q, any negative integer works except -1. That means you're supposed to shade in all of B except for a single point. Somehow you'll have to convey that that's what's meant to be shaded in. It's easy to see that the only element of R is 0, so a single point in C, but not in A or B, is what is needed here.

For T, if you do the working out, you find that no element of T is in either A,B or C, so the area they want you to shade is an area outside C. And with that, I hope I've been helpful. At least you should probably have some idea where I'm coming from, anyway.