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Problem 3. A function f : X→ Y is surjective (also known as onto) every element of Y has a preimage: Vy Y3 € X f(x) = y. Suppose f: A → B and g : B → C are both surjective. Let h: A → C be defined as h(x) = g(f(x)). Prove that h is surjective. In your proof, in addition to the logic rules, you are allowed to use the definition of h, and the following rules about equality: applying a function to equal values gives the same result; and if two terms are equal, one can be substituted in place of the other.

Problem 3. A function f : X→ Y is surjective (also known as onto) every element of Y has a preimage: Vy Y3 € X f(x) = y. Suppose f: A → B and g : B → C are both surjective. Let h: A → C be defined as h(x) = g(f(x)). Prove that h is surjective. In your proof, in addition to the logic rules, you are allowed to use the definition of h, and the following rules about equality: applying a function to equal values gives the same result; and if two terms are equal, one can be substituted in place of the other.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Problem 3. : A function f X→Y is surjective (also known as onto) every element of Y has a preimage: Vy E Y 3x EX f(x) = y. Suppose f: A B and g: B C are both surjective. Let h: AC be defined as h(x) = g(f(x)). Prove that h is surjective. In your proof, in addition to the logic rules, you are allowed to use the definition of h, and the following rules about equality: applying a function to equal values gives the same result; and if two terms are equal, one can be substituted in place of the other.
Transcribed Image Text:Problem 3. : A function f X→Y is surjective (also known as onto) every element of Y has a preimage: Vy E Y 3x EX f(x) = y. Suppose f: A B and g: B C are both surjective. Let h: AC be defined as h(x) = g(f(x)). Prove that h is surjective. In your proof, in addition to the logic rules, you are allowed to use the definition of h, and the following rules about equality: applying a function to equal values gives the same result; and if two terms are equal, one can be substituted in place of the other.
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