This is what I wrote...initially I wanted to write that it is false because an axiom is a basic property and wouldn't be so basic if you start combining them.
In the axioms for a vector space, can Axioms (2) and (3) be replaced by a single axiom that states $(u + v) + w = v + (u + w)$
Recall that axioms (2) and (3) for a vector space are:
(2) For all $u$ and $v \in V$, $u + v = v + u$. (Commutativity of vector addition)
(3) For any three vectors $u,v,$ and $w$, $(u + v) + w = u + (v + w)$. (Associativity of vector addition)
Yes, we can combine the axioms of commutativity and associativity into one single axiom since in order to get from the left hand side of the equation to the right hand side of the equation the idea of commutativity and associativity are displayed as follows:
$(u + v) + w = u + (v + w) =$.................................( associativity axiom)
$(u + v) + w =$.................................(associativy axiom again)
$(v+u) + w =$....................................(commutitivity axiom)
$v + (u + w)$
Therefore the above axiom has the axioms (2) and (3) combined into one axiom.
Thanks.