7. (1 point) Complete the following proof by selecting a suitable statement to l

Question

7. (1 point) Complete the following proof by selecting a suitable statement to ll the dotted space. Suppose x is rational and y is irrational. Then x = a/b for some integers a,b with b not equaled to 0. Now assume to get a contradiction that x+y is rational. Then x+y = c/d for some integers c,d with d not equaled 0. Then y = (x+y)x = c/d a/b = bcad/ bd is rational as well. 1. That contradicts the assumption that y is irrational. Therefore....... • A. y is rational. • B. x+y is rational. • C. y is irrational. 2 • D. x+y is irrational. • E. none of these. • F. x is rational. • G. x is irrational.

Explanation / Answer

Answer:

The answer is x+y is rational.

If x is rational and y is irrational then their sum x+y is irrational.

If both x and y are rational then their sum x+y is rational

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