Question

If a is a negative rational number and b is a positive rational number, which of the following must be true?

Give an example for the statements that are true
Give a counterexample for the statements that are false.

a. a-b is positive
b. b-a is positive
c. b+(-a) is negitive

Answer 1

Answer choice B is positive. Subtracting a negative number is a double negative, or a positive. An example of this is 5-(-3)=5+3=8. Choice A is wrong, because -3-5=-8, and subtracting any positive number from a negative number will wield a negative number. Choice C is wrong because 5+(-3)=5-3=2, which is not always negative as seen here (although if the absolute value of -a is greater than b, it WILL be negative). Hope this helped!