ok here is my revised attempt at the answer with your help:
In order to prove that (X⊕Y)⊕(Y⊕Z) = X⊕Z you must imply that ⊕ forms a group operation this proof is split up into three parts
The symmetric difference is associative which means that
(X⊕Y)⊕(Y⊕Z)= (Y⊕Y)⊕(X⊕Z) --I think that...
Homework Statement
There is a symmetric difference in sets X & Y, X Y is defined to be the sets of elements that are either X or Y but not both
Prove that for any sets X,Y & Z that
(X\oplusY)\oplus(Y\oplusZ) = X\oplusZ
Homework Equations
\oplus = symmetic difference
The Attempt at...
for 4) {x : x is a real number strictly between − i and i}.
would it be:
a0 {0}
a1 {-1,1}
a2 {-2,2}
a3 {-3,3}
a4 {-4,4}
a5 {-5,5}
union: {0,-1,1,-2,2,-3,3,-4,4,-5,5,...}
intersection: empty set
correct?
no i do not...
so would a0 then be {(0, 1),...} etc
then would the union be
{(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),...} or {0,1,2,3,4,5,6,...}
i imagine the intersection would be \emptyset whichever way
...ok now I am stuck on 3) {x : x is a real number such that i < x < i + 1}
how do you list the x?
do you have to declare it?
or do you just leave it as x i think I am barking up the wrong tree but this is what i have got thus far...
a0 = {0,x,1,...}
a1 = {1,x,2,...}
a2 = {2,x,3,...}
a3 =...
for 2) Ai = {0, i, 2i}
A0 {0,0,0}
A1 {0,1,2}
A2 {0,2,4}
A3 {0,3,6}
A4 {0,4,8}
A5 {0,5,10}
Would \bigcup_{i=0}^{\infty} A_{i} simply be {0,1,2,3,4,5,6,8,10}
would \bigcap_{i=0}^{\infty} A_{i} be {0}?
ok
1)
A0 {0,1,-1,2,-2,...}
A1 {1,-1,2,-2,...}
A2 {-1,2,-2,...}
A4 {2,-2,...}
A5 {-2,...}
think that right probably not...
Would \bigcup_{i=0}^{\infty} A_{i} simply be {0,1,-1,2,-2,...} ?
would \bigcup_{i=0}^{\infty} A_{i} be {-2,...}?
...ok i need to find \bigcup_{i=0}^{\infty} A_{i} & the \bigcap_{i=0}^{\infty} A_{i} for each
i can see that A0 is a set of integers
would the union be?
A0 \bigcup_ A1 = {0,1,-1,2,-2,...}
and the intersection?
A0 \bigcap_ A1 = {1,-1,2,-2,...}
is that it for question one...
Homework Statement
Find ∪i=0Ai (with infinite symbol) and ∩ i=0Ai (with infinite symbol) in each of the cases when for each natural number
i, Ai is defined as:
1. Ai = {i,−i, i + 1,−(i + 1), i + 2,−(i + 2), . . .}
2. Ai = {0, i, 2i}
3. Ai = {x : x is a real number such that i < x...