# sets

• Oct 22nd 2005, 04:57 AM
alexis
Right then who can do this tuff cookie (3)
3. Let A = [0,1) = {x: 0 <= x<1} and B = [-1/2, 1/2] = {x: -1/2 <= x <= 1/2}

Identify the following sets:

(i) AUB
(ii) AnB
(iii) A'
(iv) B'

Find (AUB)' and show this set is A' n B'. Prove generally that (AUB)' = A' n B'

EXTENSION

The symmetric difference between two sets is defined as

A (small triangle, can't type it) B = (A - B) U (B-A)

(a) Draw Venn Diagrams to show that this is equivalent to (AUB) - (AnB)

(b) Prove (algebraically) that (A-B) U (B-A) = (AUB) -(AnB)

(c)If A is the set of even integers and B the set of integers which are multiples of 3, describe the set (AUB) - (AnB)
• Oct 23rd 2005, 06:00 AM
hpe
Quote:

Originally Posted by alexis
3. Let A = [0,1) = {x: 0 <= x<1} and B = [-1/2, 1/2] = {x: -1/2 <= x <= 1/2}

Identify the following sets:

(i) AUB
(ii) AnB
(iii) A'
(iv) B'

Draw some pictures. Then try to describe the sets with simple sets of inequalities. Then prove your results. For (iii) and (iv) you need to specify a set in which to take the complement (the set of real numbers?).

As a general comment, you ought these problems yourself and identify the stumbling blocks before posting homework assignments wholesale. I'd be happy to help you when you get stuck, but not earlier.
• Oct 25th 2005, 07:13 AM
alexis
Need help with these sets and relations question
Right I am stuck on this question....

The symmetric difference between two sets is defined as

A (triangle, can't type it sorry!) B = (A-B) U (B-A)

(b) Prove (algebraically) that (A-B) U (B-A) = (AUB) -(AnB)
(c)If A is the set of even integers and B the set of integers which are multiples of 3, describe the set (AUB) - (AnB)

Can someone come up with the answer for this as I cannot do it at all, done the rest??? :)
• Nov 28th 2005, 10:31 PM
lewisje
b) The left side consists of all elements of A that are not in B and all elements of B that are not in A; the right consists of all elements that are in A or B but not both. It is not hard to prove generally that they are equal.

c) This is the set of integers that are multiples of 2 or 3 but not 6. You could also think of it as the set of integers that differ from an odd multiple of 3 by at most 1...here are the first few positive elements of this set: 2, 3, 4, 8, 9, 10, 14, 15, 16,...