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

Q8 – 6 points Definition: Given sets A and B, the symmetric difference of A and B, denoted as A △ B, is A △ B = (A – B) ∪ (B – A) Let A = {1, 3, 4}  and  B = {1, 2, 4, 5, 6}. Find A △ B.

Q10- 6 points Is the following sentence a statement? Explain why or why not? If a positive integer has a negative square, then it is prime. 

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

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 A2 = {n ∈ Z | n = 3k + 2, for some integer k}. Is {A0, A1, A2}  a partition of Z? Explain why or why not?

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Q1 – 9 points Let A = { h, j, k, l, m }, B = { m, n }, and C = { k, m } Is  B ⊆ A? Is  A ⊆ C? Is C a proper subset of C?

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

Q10- 6 points Is the following sentence a statement? Explain why or why not? If a positive integer has a negative square, then it is prime. 

I have read and understand the syllabus for this course