A. a vector is any element of a vector space. is this statement true or false?
a. true by the definition of a vector space
b. false; not all vectors are elements of a vector space.
c. false; a vector space is any element of a vector.

A. True by the definition of a vector space

Explanation:

Vector space is the collection of the objects which is known as vectors, that may be added together or can be multiplied by the numbers which are known as scalars.

If vector space is a subset, then the vector is its element. Since from the definition also, vector space contains vector and a vector can be a subset.