Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using a direct proof. (a) The product of two rational numbers is a rational number. Solution (b) The quotient of a rational number and a non-zero rational number is a rational number. Solution (c) If x and y are rational numbers then is also a rational number.

See Explanation

Step-by-step explanation:

(a) Proof: Product of two rational numbers

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

The product:

Proved, because 1/3 is rational

(b) Proof: Quotient of a rational number and a non-zero rational number

Using direct proofs.

Let the two rational numbers be A and B.

Such that:

The quotient:

Express as product

Proved, because 3/4 is rational

(c) x + y is rational (missing from the question)

Using direct proofs.

Let x and y be

Such that:

The sum:

Take LCM

Proved, because 7/6 is rational

The above proof works for all values of A, B, x and y; as long as they are rational values

javeir earned 56 dollors more than kyle so kyle and javier had 14w but javier made 56 dollors more so 14w plus 56 equals 70w so kyle has 14w

step-by-step explanation: hope i plz give me brainliest with the points so this is not constant cause it says last week so its clearly not every week

answer:

your answer is: c. 196 7/8 in^3.