Question

exercise 2.4.9. [used in theorem 2.7.1.] let a b , c d ∈ q. prove that a if either cb−ad > 0 and bd > 0, or cb−ad < 0 and bd < 0.

Answer 1

To prove the statement, we consider two cases: when cb-ad > 0 and bd > 0, or when cb-ad < 0 and bd < 0. In both cases, we can conclude that the fractions a/b and c/d have the same sign.

Step-by-step explanation:

In order to prove the statement, let's consider two cases:

Case 1: If cb - ad > 0 and bd > 0

Since both cb - ad > 0 and bd > 0, we can conclude that both fractions a/b and c/d are positive

Case 2: If cb - ad < 0 and bd < 0

Since both cb - ad < 0 and bd < 0, we can conclude that both fractions a/b and c/d are negative

Therefore, in both cases, we have proved that if either cb - ad > 0 and bd > 0, or cb - ad < 0 and bd < 0, a/b and c/d have the same sign.