1: Each of the following sets, X, ARE NOT vector spaces over the given field F and with the given operations. List, with justification, all vector space axioms failed by the sets. (a) X is the open upper half plane in R: X X = { [C] R \y >0} and both vector addition and scalar multiplication are the same as in R. (b) The set X are given by = R2 over the field F = R where vector addition and scalar multiplication a 6+3-8+3 = a+c b+d a and C [8] = [ca] (c) X - Rover FZ2 where vector addition is the same as in R and scalar multiplication is given by 0 x = 0 and 1 x = x.