A security analyst is verifying a property of an encryption key generation algorithm. The analyst needs to prove the following statement:
'For every non-zero rational number α\alphaα and every irrational number β\betaβ, the result of the calculation 5αβ\frac{5\alpha}{\beta}β5α is always an irrational number.'
Identify the correct starting assumption for a proof by contradiction of this statement.
- There exists a non-zero rational number α\alphaα and an irrational number β\betaβ such that 5αβ\frac{5\alpha}{\beta}β5α is rational.
- For all non-zero rational numbers α\alphaα and all irrational numbers β\betaβ, the value 5αβ\frac{5\alpha}{\beta}β5α is rational.
- There exists a non-zero rational number α\alphaα and an irrational number β\betaβ such that 5αβ\frac{5\alpha}{\beta}β5α is irrational.
- For all non-zero rational numbers α\alphaα and all irrational numbers β\betaβ, the value 5αβ\frac{5\alpha}{\beta}β5α is irrational.
