Are the following subsets subspaces of the given vector space?Justify your answers using words and proper…

Are the following subsets subspaces of the given vector space?Justify your answers using words and proper mathematical notation. If the set is not a subspace of the given vector space, give a counterex- ample (an example that demonstrates that one of the axioms fails) and explain why this shows the subset is not a subspace. If the set is a subspace, then prove it by showing that the conditions for a subset to be a subspace are met (a) S (a, b, c) :a b+c), V-R3 (b) S (a, b, c): a +b+c 1)