What Are the Solutions to These Set Theory Problems?

[lorik]

Homework Statement

Have the notebook in here but can't connect what's really happening AND very easy stuff ?
for example :
1) if A={a,b,c}
A U B={a,b,c,d,e}
A\B={a,b}
B=?

2) n(A)=12
n(B)=10
n(A U B)=18
n(A\B)=?
3)This one is tricky
n(A)=4*n(B)
n(A\B)=20
A 'oposite of U' B= 16
B\A=?

Homework Equations

The Attempt at a Solution

1)?
2) n(A U B)=n(A)+n(B)-n(A 'oposite of U' B)
18 = 12+10-n(A 'oposite of U' B)
n(A 'oposite of U' B)= 8 <------------- IS THIS CORRECT BECAUSE IF i DO IT MYSELF IT TURNS OUT 4 NOT 8 ,please confirm

3) n(A)=4*n(B)
24 why and how ?# 24 =4*n(B) /:4
N(B)=6
m(B\A)=2 <-------------AGAIN HOW CAN IT BE 2 ??


And also is there more info I can find in wikipedia about set theory if you know a link please send it to me. Thanks you

 

[nate808]

Hello,

It seems like you are struggling to understand the concepts of set theory. Let's break down each of the problems and go through them step by step.

1) If A={a,b,c} and A U B={a,b,c,d,e}, then we can deduce that B={d,e}. This is because the union of two sets includes all elements from both sets. Since A already includes {a,b,c}, the additional elements in A U B must come from B, which are {d,e}.
Similarly, if A\B={a,b}, then we can deduce that B={c,d,e}. This is because the difference of two sets includes all elements in the first set but not in the second set. Since A already includes {a,b}, the additional elements in A\B must come from B, which are {c,d,e}.

2) We are given that n(A)=12, n(B)=10, and n(A U B)=18. To find n(A\B), we can use the formula n(A U B)=n(A)+n(B)-n(A 'opposite of U' B). This is because the union of two sets includes all elements from both sets, but we must subtract the elements that are in both sets to avoid counting them twice. In this case, n(A U B)=18, n(A)=12, and n(B)=10, so we can plug these values into the formula and solve for n(A 'opposite of U' B).

n(A U B)=n(A)+n(B)-n(A 'opposite of U' B)
18=12+10-n(A 'opposite of U' B)
n(A 'opposite of U' B)= 8

So, n(A 'opposite of U' B)=8, which means that there are 8 elements that are in both sets A and B.

3) We are given that n(A)=4*n(B) and n(A\B)=20. To find A 'opposite of U' B, we can use the formula n(A)=n(A 'opposite of U' B)+n(A 'opposite of U' B). This is because the union of two sets includes all elements from both sets, but we must subtract the elements that are in both sets to avoid counting them twice. In this case, n(A)=4*n(B) and n(A\B