A+ Work

4. (10 pts) Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive:

    a.       

    b.    

    c.     

5. (10 pts) Determine whether the following pair of statements are logically equivalent. Justify your answer using a truth table.

6. (10 pts) Prove or disprove the following statement:
, if n is even and m is odd, then n + m is odd

7. (10 pts) Prove the following by induction:

8. (10 pts) Use the permutation formula to calculate the number permutations of the set {V, W, X, Y, Z} taken three at a time. Also list these permutations.

9. (10 pts) Translate the following English sentences into statements of predicate calculus that contain double quantifiers and explain whether it is a true statement.

10. (10 pts) Consider the following graph:

Is this a simple graph? 


Does this graph contain any cycles? 


Does this graph contain an Euler cycle?