Question

prove that AUB=A & intersection of A&B=A then A=B

Answer 1

x belongs to AUB = A => x belongs to A or x belongs to B = x belongs to A ... which implies B is subset of A

Answer 2

for other part, what does & symbol imply??

Answer 3

& if x belongs to B then A is a subset of A, and as A & B are both subsets of eachother then A=B

Answer 4

is that intersection??

Answer 5

A∩B=A

Answer 6

oh ...
x belongs to A and x belongs to B = x belongs to A => implies A is subset of B

so if A is subset of B and B is subset of A, then A = B

Answer 7

I am not sure if those two first steps are right though.

Answer 8

hmmmm that's the reason I was looking for solution manual of Kolmogorov's analysis :( thanks anyway

Answer 9

@experimentX
1) A U B = A then prove A =B
let x ∈ A U B
x ∈ (A) U (B)
then by axiom we know that x belongs to at least one set i.e. x belongs to either A or to B or to both,
i.e. x∈A or and x ∈ B
=> A⊂B & B⊂A
hence A=B

Answer 10

Oo ..