Prove or disprove that if a and b are two rational numbers, then a b is also a rational number.

That is not correct, In a quotient or any type of equation numbers are considered rational number when they have repeating values, for this we will use {x} for example when comparing repeating values.

So if we have {a} + {b} from a equation prior to obtaining these values then we will take {a} + {b} and add {c} we will end up with {a} + {b} + {c}. We are using addition for an example.

{c} would only be a rational if it as well had repeating {x} values

{x}=Repeating value