In each of the following, determine whether the indicated addition and scalar multiplication on ordered pairs of real numbers yields a vector space. For those that are not vector spaces, determine which properties of a vector space fail to hold.
a) (x1, y1) + (x2, y2) = (x1, y2), c(x, y) = (cx, cy)
b) (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2), c(x, y) = (c + x, c + y)
c) (x1, y1) + (x2, y2) = (x1 + y2, x2 + y1), c(x, y) = (cx, cy)
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