Question 418456
(a) Under the standard operations of addition and multiplication, the set of all real numbers follows the closure, distributive, associative, additive inverse, and identity element properties.  It also follows the usual distributive laws.  Therefore R is a vector space.

(b)The set of all pairs of real numbers of the form (x,0), with standard operations on R^2 is isomorphic to R, and hence is also a vector space.