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Instructions: • Write your solutions and answers clearly and legibly on any paper. . Do not use pencil. A. Let A = {-2,-1,0,1,2), B = {1,2,5}, C = {n² ER:n e A}. For items (1)-(4), write TRUE if the statement below is true, write FALSE otherwise. (1) (2) (3) (4) Statement: -2 A. Statement: BCA. - The statement "For every natural number n, n is positive" is equivalent to Vn € N, n ≥ 0. . The statement "If x² = 9, then x=3 or r=-3" is a conditional statement. For iteme (5)-(9) define a relation R from 4 to R as follows: Given any (1) AVR pm (

Instructions: • Write your solutions and answers clearly and legibly on any paper. . Do not use pencil. A. Let A = {-2,-1,0,1,2), B = {1,2,5}, C = {n² ER:n e A}. For items (1)-(4), write TRUE if the statement below is true, write FALSE otherwise. (1) (2) (3) (4) Statement: -2 A. Statement: BCA. - The statement "For every natural number n, n is positive" is equivalent to Vn € N, n ≥ 0. . The statement "If x² = 9, then x=3 or r=-3" is a conditional statement. For iteme (5)-(9) define a relation R from 4 to R as follows: Given any (1) AVR pm (

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Instructions: .Write your solutions and answers clearly and legibly on any paper. . Do not use pencil. A. Let A = {-2,-1,0,1,2}, B = {1,2,5}, C = {n² € R:n € A}. For items (1)-(4), write TRUE if the statement below is true, write FALSE otherwise. (1) (2) (3) Statement: -2 € A. Statement: BC A. The statement "For every natural number n, n is positive" is equivalent to Vn € N, n ≥ 0. The statement "If r² = 9, then r = 3 or x = -3" is a conditional statement. For items (5)-(9), define a relation R from A to B as follows: Given any (x, y) = A x B₁ (x, y) = R iff y = 2² +1. (5) State explicitly the elements of C (write set C in set-roster notation) (6) State explicitly which ordered pairs are in Cartesian Product A x B. (7) State explicitly which ordered pairs are in the relation R. (8) What are the domain and co-domain of R? (9) Is A x B C R? Why or why not? B. Let N be the set of natural numbers, A = {(¹, , , , }, B = { ½ : 1 ≤ x ≤ 10, where a € N}. (10) State explicitly the elements of the set B (write set B in set-roster notation). (11) Write set A in set-builder notation (follow the format A = {z € X : P(x)}). For items (12)-(14), Let the mapping F: N→ A be defined as F(x) = ¹. (12) Evaluate F (10) (13) Evaluate 100-F (5) - 20. (14) Is the mapping F a function? Why or why not? C. Negate the following statements and re-express the result in equivalent positive form: I have already tasted all the items in the food menu. D. Suppose is a binary operation from Zx N to Z defined by m* n = m² + 2n. Evaluate m * n if m= -7 and n = 10.
Transcribed Image Text:Instructions: .Write your solutions and answers clearly and legibly on any paper. . Do not use pencil. A. Let A = {-2,-1,0,1,2}, B = {1,2,5}, C = {n² € R:n € A}. For items (1)-(4), write TRUE if the statement below is true, write FALSE otherwise. (1) (2) (3) Statement: -2 € A. Statement: BC A. The statement "For every natural number n, n is positive" is equivalent to Vn € N, n ≥ 0. The statement "If r² = 9, then r = 3 or x = -3" is a conditional statement. For items (5)-(9), define a relation R from A to B as follows: Given any (x, y) = A x B₁ (x, y) = R iff y = 2² +1. (5) State explicitly the elements of C (write set C in set-roster notation) (6) State explicitly which ordered pairs are in Cartesian Product A x B. (7) State explicitly which ordered pairs are in the relation R. (8) What are the domain and co-domain of R? (9) Is A x B C R? Why or why not? B. Let N be the set of natural numbers, A = {(¹, , , , }, B = { ½ : 1 ≤ x ≤ 10, where a € N}. (10) State explicitly the elements of the set B (write set B in set-roster notation). (11) Write set A in set-builder notation (follow the format A = {z € X : P(x)}). For items (12)-(14), Let the mapping F: N→ A be defined as F(x) = ¹. (12) Evaluate F (10) (13) Evaluate 100-F (5) - 20. (14) Is the mapping F a function? Why or why not? C. Negate the following statements and re-express the result in equivalent positive form: I have already tasted all the items in the food menu. D. Suppose is a binary operation from Zx N to Z defined by m* n = m² + 2n. Evaluate m * n if m= -7 and n = 10.
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