MATH SOLVE

3 months ago

Q:
# 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.

Accepted Solution

A:

Answer: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.Step-by-step 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 ==== rationalif y = 2 ==== rationalx+y = 7 ==== rationalbut, ifx = 1.333333......... ======irrationaly = 5 =======rationalx+y = 6.3333333.... = irrational