Show your steps and explain your answers clearly. Show whether or not each of the following sets V=(G,F) are valid vector spaces. Except in part e), the group operator is parallelogram "vector" addition. 1. G is the set of points (x,y) in the Cartesian plane such that y=3x+2. F is the field of real numbers. 2. G is the set of points in the Cartesian plane containing only the zero element (x=0,y=0),F is again the reals. 3. G is the set of points in the Cartesian plane (x,y) such that y=x32x. F is the reals. 4. G is the set of all points (x,y) in the Cartesian plane. F is the reals. 5. G is the set of ordered pairs (p,q) where p and q each belong to corresponding vector spaces P and Q, which are both vector spaces over the same field F. For each p1,p2 in P and each q1,q2 in Q, define the sum ( operation) of two elements in G by (p1,q1)+(p2,q2)=(p1+p2,q1+q2). Scalar multiplication is defined by (p1,q1) =(p1,q1), for any in F