Discrete mathematics subsets Suppose I have two sets A and B:
$$ A = \lbrace 2k-1 : k \in \mathbb{Z}\rbrace$$ 
$$ B = \lbrace 2l+1 : l \in \mathbb{Z}\rbrace$$ 
I need to prove that A = B. 
I know that to prove equality between two sets I need to prove both:
$$ A \subseteq B $$
and
$$ A \supseteq B $$
I tried to start with something like :
Suppose x is an element of A, then 
$$ x = 2k - 1 $$
EDIT : Which we can rewrite as
$$ x = 2k + 1 - 2$$
$$ x  = 2(k-1) + 1$$
Because $$ (k-1) \in \mathbb{Z} $$
We know that x is also in B.
Is this the correct way of approaching this problem?

Hint: 


*

*$2k-1=2l+1$ where $l=(k-1)$;

*$2l+1=2k-1$ where $k=l+1$.

