Discrete Mathematics

1. Question 1:

Provide the truth table for the following propositional logic: (PQ) P (Q P)

2. Question 2:

Show that P ( Q P) is a tautology or no? (Without using truth table)

3. Question 3:

Translate the following into propositional logic: (specify the atomic positions)

All PSU students are Smart

If you pass the CS285 course then you will be a good engineer

No CS285 student will fail the course

4. Question 4:

Let set A = { 1,2,3,4,5,6} and B = {2,3,5,6,7,8 }

A B =

A U B =

A B =

5. Question 5:

Verify if the following function is bijective. f: R R f(x) = x² 3

6. Question 6:

Is the following function invertible? If yes provide the inverse

Let f a function from R to R, such that f(x) = 5 / (2 x)