Prove the following proposition. For all real numbers x and y, if x is rational and...

 

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Prove the following proposition. For all real numbers x and y, if x is rational and y is irrational, then x+y is irrational. Proof. We will prove this using [Select] and x+y is [Select] X = and x+y=. Then y = (x + y) - x = [Select] [Select] . By definition, there exist integers a, b, c, and d, such that . Assume x is rational, y is irrational, which is a contradiction. V So y must be Prove the following proposition. For all real numbers x and y, if x is rational and y is irrational, then x+y is irrational. Proof. We will prove this using [Select] and x+y is [Select] X = and x+y=. Then y = (x + y) - x = [Select] [Select] . By definition, there exist integers a, b, c, and d, such that . Assume x is rational, y is irrational, which is a contradiction. V So y must be