Consider the following sets for all questions on this page: A={(x, y) = Z:y> 0 and...

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Consider the following sets for all questions on this page: A={(x, y) = Z²:y> 0 and r = 2k for some k € Z} B = {(x, y) = Z²2:y> 0 or r = 2k for some k € Z} D = {(x, y) € 2²:20 <r²<50, y = 2r + 1} (1) [5 pts] Express the set D by listing all elements between appropriate braces. (2) [6 pts] Express the set DA by listing all elements between appropriate braces. (3) [6 pts] Express the set D- B by listing all elements between appropriate braces. (4) [4 pts] Is the following statement True or False? D-A=D (BOA) (5) [6 pts] Express four (4) elements of the set P(D) x P(A). (6) [4 pts] Find |P(D) × P(D)|. (7) [10 pts] Is the following statement True or False? V(r. y) E D, 3(w, 2) EB, y = 2w+1 (8) 5 pts] Is the following statement True or False? 3(w.) € B.V(r.y) E D₁w=2w + 1 (9) [5 pts] Draw a Venn diagram for the following set: ((A-B) UC) n(An (C-B)) (10) [5 pts] Are the following logically equivalent? (PA-P)⇒Q and (PV (QA-Q)) ⇒ P s (11) [10 pts] Negate the following statement, then determine if the negation is True or False. For all real numbers a, there exists a real number such that ya only if y2 r. (12) [9 pts] Let A, = {-2i, 0, 2i}, B = [i, i + 1], and I = {r € N:2² <10}. Sketch the following set in R²: UA₁ x B₁ IEI Consider the following sets for all questions on this page: A={(x, y) = Z²:y> 0 and r = 2k for some k € Z} B = {(x, y) = Z²2:y> 0 or r = 2k for some k € Z} D = {(x, y) € 2²:20 <r²<50, y = 2r + 1} (1) [5 pts] Express the set D by listing all elements between appropriate braces. (2) [6 pts] Express the set DA by listing all elements between appropriate braces. (3) [6 pts] Express the set D- B by listing all elements between appropriate braces. (4) [4 pts] Is the following statement True or False? D-A=D (BOA) (5) [6 pts] Express four (4) elements of the set P(D) x P(A). (6) [4 pts] Find |P(D) × P(D)|. (7) [10 pts] Is the following statement True or False? V(r. y) E D, 3(w, 2) EB, y = 2w+1 (8) 5 pts] Is the following statement True or False? 3(w.) € B.V(r.y) E D₁w=2w + 1 (9) [5 pts] Draw a Venn diagram for the following set: ((A-B) UC) n(An (C-B)) (10) [5 pts] Are the following logically equivalent? (PA-P)⇒Q and (PV (QA-Q)) ⇒ P s (11) [10 pts] Negate the following statement, then determine if the negation is True or False. For all real numbers a, there exists a real number such that ya only if y2 r. (12) [9 pts] Let A, = {-2i, 0, 2i}, B = [i, i + 1], and I = {r € N:2² <10}. Sketch the following set in R²: UA₁ x B₁ IEI

Answer rating: 100% (QA)

Given the sets A xy Z y 0 and x 2k for some k Z B xy Z y 0 or x 2k for some k Z D xy Z 20 x 50 y 2x1 1 We have to list all elements of D For x 2 we must find the perfect squares between 20 and 50 whic... View the full answer