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?

Your approach is correct, but just to help give you an example in writing out your mathematical argument to give you some confidence, I would write it like this:
Suppose $x \in A$. Then there exists a $k \in \mathbb{Z}$ such that $x = 2k - 1 = 2l + 1$ where $l = k - 1$ (following the hint above/what you wrote). Since $k \in \mathbb{Z}$, $l \in \mathbb{Z}$, so $x \in B$.
See if you can write out the $B \subseteq A$ direction. Hope that helps!
