Q3-10 points Use truth tables (only) to determine whether the following argument is valid or invalid, justify your answer:                                                                                          

Q5-5 points Consider the statement “The square of any odd integer is odd.” Rewrite the statement in the form ∀ _____ n, if ____ then ____ . (Make sure you use the variable n when you fill in each of the second two blanks.)

Q10-8 points Let

Q6-5 points Which of the following is a negation for “There exists a real number x such that for all real numbers y, xy > y.”  

Q5-5 points Consider the statement “The square of any odd integer is odd.” Write a negation for the statement.

Q9- 6 points Use an element argument to prove the following statement: For all sets A and B, if A ⊆ B, then BC ⊆ AC.

Q5 – 6 points Let A = {p, q, r}, B = {0, 1, 3}, and C = {0, 4}. Use set-roster notation to write the following set: A × (B ∪ C).    

Q7- 6 points Consider the following statement: For all sets A and B, (A ∪ B) ∩ C  =  A ∪ (B ∩ C) Write a sentence that describes what would be required to show that this statement is false, and find subsets of {1, 2, 3, 4, 5, 6} which can be used to meet that requirement.

Q12 – 6 points Draw a Venn diagram for sets A, B and C satisfying the following conditions: A ⊆ C, B ⊆ C, A ∩ B = ∅.

Q3 – 6 points Let Z be the set of all integers and let  A0 = {n ∈ Z | n = 3k, for some integer k} A1 = {n ∈ Z | n = 3k + 1, for some integer k}  and Is {A0, A1}  a partition of Z? Explain why or why not?