A cybersecurity expert is verifying a protocol where a security key $k\,$ is generated as the quotient $k=μσ\displaystyle k = \frac{\mu}{\sigma}$ , where $\mu\,$ is a non-zero rational coefficient and $\sigma\,$ is an irrational physical constant. To establish the security of the protocol, the expert wishes to use proof by contradiction to prove the statement:

'The quotient of a non-zero rational number and an irrational number is always irrational.'

Identify the correct starting assumption for the expert's proof.

For all non-zero rational $\mu\,$ and irrational $σ\sigma$ , the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is rational.
There exists a non-zero rational $\mu\,$ and an irrational $\sigma\,$ such that the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is rational.
There exists a non-zero rational $\mu\,$ and an irrational $\sigma\,$ such that the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is irrational.
For all non-zero rational $\mu\,$ and irrational $σ\sigma$ , the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is irrational.

'The quotient of a non-zero rational number and an irrational number is always irrational.'

Identify the correct starting assumption for the expert's proof.

For all non-zero rational $\mu\,$ and irrational $σ\sigma$ , the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is rational.
There exists a non-zero rational $\mu\,$ and an irrational $\sigma\,$ such that the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is rational.
There exists a non-zero rational $\mu\,$ and an irrational $\sigma\,$ such that the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is irrational.
For all non-zero rational $\mu\,$ and irrational $σ\sigma$ , the quotient $μσ\displaystyle \frac{\mu}{\sigma}$ is irrational.

Algebraic Methods

Question 47

Markscheme

Algebraic Methods

Question 47

Markscheme

Algebraic Methods

Question 47

Algebraic Methods Questions

Algebraic Methods

Question 47

Algebraic Methods Questions