Question 1. Let A and B are two sets. Let D be the set defined by:...

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Question 1. Let A and B are two sets. Let D be the set defined by: (a) The elements that are either in set A or in set B but not in both sets A and B. (b) (c) (A\B) U (B\A) (A U B)\(An B) Do you think that all of these sets in (a), (b) and (c) represent the same set? Explain D by some figure or Venn diagram if possible. Question 2. Let An = {(n + 1)k | kE N}. Find A1, A2, A3 and also find A, n A2 and A2 n A3. Question 3. Let A = {1,2,3} , B = {x €R |1 < x < 2} and C= {x € R | 2 < x < 3}. Find A x B and B x C. %3D Question 4. Let S = {1,2,3} and T = {a, b}. Find some iniections and surjections from S to T. Question 5. Prove by mathematical induction that 2" < n! For all n 2 4. Question 6. Determine the following sets of real numbers. A = {x € R | x² > 3x + 4} B = {x € R |1 < x² < 4}. Question 1. Let A and B are two sets. Let D be the set defined by: (a) The elements that are either in set A or in set B but not in both sets A and B. (b) (c) (A\B) U (B\A) (A U B)\(An B) Do you think that all of these sets in (a), (b) and (c) represent the same set? Explain D by some figure or Venn diagram if possible. Question 2. Let An = {(n + 1)k | kE N}. Find A1, A2, A3 and also find A, n A2 and A2 n A3. Question 3. Let A = {1,2,3} , B = {x €R |1 < x < 2} and C= {x € R | 2 < x < 3}. Find A x B and B x C. %3D Question 4. Let S = {1,2,3} and T = {a, b}. Find some iniections and surjections from S to T. Question 5. Prove by mathematical induction that 2" < n! For all n 2 4. Question 6. Determine the following sets of real numbers. A = {x € R | x² > 3x + 4} B = {x € R |1 < x² < 4}.