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For each set, list two elements of the set, and then slum that the set doe not form a vector space by specifying the axiom that it does not satisfy, demonstrating this with a specific counter-example if appropriate. A= {(x, y, z) | x, y, z ER and x + y + z = 1}. B = {(x y 1 z)|x, y, z ER}. C = {ax2 + bx + c | a, b, c ER+ }, where R+ is the set of positive real numbers. D = {(x, y) | x, y ER and either x + y = 0 or else x + y = 2}.
Show transcribed image text For each set, list two elements of the set, and then slum that the set doe not form a vector space by specifying the axiom that it does not satisfy, demonstrating this with a specific counter-example if appropriate. A= {(x, y, z) | x, y, z ER and x + y + z = 1}. B = {(x y 1 z)|x, y, z ER}. C = {ax2 + bx + c | a, b, c ER+ }, where R+ is the set of positive real numbers. D = {(x, y) | x, y ER and either x + y = 0 or else x + y = 2}.