# Expert Answers

1. (10 pts) Determine whether the following binary relations are reflexive, symmetric, antisymmetric and transitive:

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?

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?

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