Question

Linear Algebra:

Answer 1

For sets A and B,
\[A = B\] If and only if\[A \subseteq B\] and \[B \subseteq A\]

How can I show this is true?

Answer 2

You have to go both ways
if you have p <->q statement, then you will need to prove p->q then also q->p

Answer 3

But isn't that the definition of equality of two sets?

Answer 4

I think i have a method but I don't know how to go about it

Answer 5

For all X contained in A, because of A is a subset of B then X is contained in B

Answer 6

When does one need to prove definitions?

Answer 7

Not sure?

Answer 8

Johnbc needs to provide his definition of equal sets

Answer 9

I have to establish that they are equal sets but Im using the A is a subset of B in my definition and I dont think I should be?
Almost like defining a word by using the word in its definition

Answer 10

?