Discrete Structures Test 1 Sample Questions

I would take the following questions "with a grain of salt."  They are taken from a different semester when I taught things with a different emphasis and are probably pushing the challenging side for how we covered things.  However, if you can get through these you should be in great shape.  You can check out an answer key for these questions.

I would also review the homework questions/answers   These are more the caliber of questions I will ask on the exam.

Finally, don't forget to check out the study guide.

Question 1. Use a truth table to show that the following wff is a tautology.

Question 2. Let A, B, and C be the following statements:

A: I am thirsty.

B: My glass is empty.

C: It is three o'clock.

Translate the following compound statements into propositional well-formed formulas.

a) I am thirsty and my glass is not empty.

b) It is three o'clock and I am thirsty.

c) If it is three o'clock, then I am thirsty.

d) If I am not thirsty, then my glass is not empty.

 

Question 3.  Write the negation of problems 2a-d in English

Question 4. Give an interpretation to prove that the following wff is not valid.

Question 6. [This one harder than anything we have done, but it is still good practice]  Consider the following verbal argument.

Every pig is smarter than every horse. Arnold is a pig. But there is an owl and Arnold is not smarter than that owl. Therefore, something is not a horse.

 Translate this argument into a predicate logic wff. Use the predicate symbols:

P(x): x is a pig

H(x): x is a horse

a: Arnold

O(x): x is an owl

S(x, y): x is smarter than y