For each of the statement below, decide whether it is true or false, and prove your claim. (a) For all a, b ≤ R, if a ≤ Q \ {0} and b & Q then ‡ ‡ Q. (b) For all x, y ≤ R, if x is irrational and y is positive and irrational, then x + √y is irrational.

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