Exercise $1.$ Using the rule of inference and logical variables, show that the following premises will lead to the

given conclusion. You should mention which rule of inference you use for each step:

Premises:

If I am elected the president of the United States, I will appoint one of my CS $310$ students as the secretary

of state.

If one of my students is appointed as secretary of states, they will donate $$1,000,000$ to the university.

The university will waive the tuition fee for CS $310$ students unless they do not receive a $$1,000,000$

donation.

A sufficient condition for CS $310$ students to go on holiday abroad is that their tuition fee is waived.

CS $310$ students do not go on holiday abroad.

Conclusion: I am not elected the president of the United States.