In all problems, F = R or F =C and V is a vector space over F. 1. We know that a subset U C V is a subspace if and only if it (i) contains the zero vector, (ii) is closed under addition and (ii) is closed under scalar multiplication. (a) Give an example of U C V which satisfies the first and second conditions, but not the third. (b) Give an example of U C V which satisfies the first and third conditions, but not the second. (c) Prove that if U satisfies the second and third conditions and it is not empty, then it satisfies all three