A student wants to use proof by contradiction to prove the following statement.

"The sum of a rational number and an irrational number is always irrational."

Identify the correct starting assumption for the proof.

Tick one box.

For all rational $a$ and all irrational $b$ , the sum $a + b$ is irrational.

There exist a rational number $a$ and an irrational number $b$ such that $a + b$ is rational.

There exist a rational number $a$ and an irrational number $b$ such that $a + b$ is irrational.

For all rational $a$ and all irrational $b$ , the sum $a + b$ is rational.

A student wants to use proof by contradiction to prove the following statement.

"The sum of a rational number and an irrational number is always irrational."

Identify the correct starting assumption for the proof.

Tick one box.

For all rational $a$ and all irrational $b$ , the sum $a + b$ is irrational.

There exist a rational number $a$ and an irrational number $b$ such that $a + b$ is rational.

There exist a rational number $a$ and an irrational number $b$ such that $a + b$ is irrational.

For all rational $a$ and all irrational $b$ , the sum $a + b$ is rational.

1 Pure Mathematics

1 Pure Mathematics Questions