Let A and B be sets. What does it mean for A and B to ?have the same cardinality There is a function from A .to B which is onto only A is not a subset of B, and B .is not a subset of A There is a function from A to B which is both one-to- .one and onto There is a function from A to B which is one-to-one only

Let A and B be sets. What does it mean for A and B to ?have the same cardinality There is a function from A .to B which is onto only A is not a subset of B, and B .is not a subset of A There is a function from A to B which is both one-to- .one and onto There is a function from A to B which is one-to-one only

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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. For nonempty sets A, B and C, let f : A → B and g: B → C be functions. (a) Prove: If g of is one-to-one, then f is one-to-one. using each of the following proof techniques: direct proof, proof by contrapositive, proof by contradiction. (b) Disprove: If go f is one-to-one, then g is one-to-one.
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Suppose U = {1, 2, 3, 4, 5, a, b, c) is a universal set with the subset A = {a, b, c, 1, 2, 3, 4). Which one of the following alternatives represents a surjective function from U to A? O a. {(1, 4), (2, b), (3, 3), (4, 3), (5, a),(a, c), (b, 1), (c, b)} O b. {(a, 1), (b, 2), (c, a), (1, 4), (2, b), (3, 3), (4, c)} O c. {(1, a), (2, c), (3, b), (4, 1), (a, c), (b, 2), (c, 3)} O d. {(1, a), (2, b), (3, 4), (4, 3), (5, c), (a, a), (b, 1), (c, 2)}
5. Prove the statement: Let X and Y be two finite sets with |X|=m and |Y|=n. If there is a one-to-one function f: X → Y, then m≤n.
I have the following question and I dont know how to approach it, so if able show step by step how to solve this: "Let A be a nonempty set. If R is a relation from A to A that is both an equivalence relation and a function,then what familiar function is R? Justify your answer"
Consider the set M = {0, 2, 4, 6} and N = {1, 3, 5, 7}. Determine if each of the following ordered pairs is a function with domain M and codomain N. If you state it is a function, then determine if it is one-to-one and/or onto. a. {(0,2), (2,4), (4,6), (6,0)} b. {(6,3), (2,1), (0,3), (4,5)} c. {(2,3), (4,7), (0,1), (6,5)} d. {(2,1), (4,5), (6,3)} e. {(6,1), (0,3), (4,1), (0,7), (2,5)}
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Enter an example of an equivalence relation R on the set X = {0, 1, 5, 6, 8} such that all of the following are true: ● • (5,0) = R; (8, 6) # R; |[1] R = 2. ●
Show both parts Don't do only one question If u don't know solution of both parts then don't select the question