Question

The true statement "If x is a rational number and y is a rational number, then the sum of x and y is a rational number" is often confused with the converse "If the sum of x and y is a rational number, then x is a rational number and y is a rational number." In this case, the converse is not always true. Which statement is false? A) If the sum of x and y is a rational number, then x must be a rational number. B) If x = 3.5 and y is a whole number, then the sum of x and y must be a rational number. Eliminate C) If x is an even integer and y is an odd integer, then the sum of x and y must be a rational number. D) If the sum of x and y is a rational number, then x may be a rational number or x may be an irrational number.

Answer 1

A

Explanation:

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Answer 2

D. if the sum of x and y is a rational number , then x may be a rational number or x may be an irrational number.

Explanation:

the statement is false because the sum of a rational number and an irrational number is always equals to irrational number.

therefore, if the sum of x and y is a rational number , then x can only be a rational number.

for example:

if x = 5 ==== rational

if y = 2 ==== rational

x+y = 7 ==== rational

but, if

x = 1.333333......... ======irrational

y = 5 =======rational

x+y = 6.3333333.... = irrational