Let f : A → B and g : B –→ C be functions. (a) Prove that if gof is one-to-one, then f is one-to-one. (b) Prove that if go f is onto, then g is onto.

Q: Let A = {1, 3, 5, 6, 7, 9, 10, 12} and B = {1, 2, 3, 5, 7, 8, 9, 11, 12}. Consider the following…

A: Given a function f: A -> B , we have to determine whether it is injection, surjection,…

Q: 3. Prove if the function f : R → R is defined by the rule f (x) = 4.x + 1 for all real numbers x,…

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Q: Exercise 2: Let f: X → Y and g: Y → Z be two bijective functions. Show that (gof)-1 = ƒ-1 o g¯1.…

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Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

Q: Let A = {1,2,...,n} and consider the functions f: A → A. a. How many functions satisfy f(1) = 1? b.…

A: This question related to function and bijection.

Q: : 4. Let f A → B be a bijective function. Construct a function g : B → A such that g(f(a)) = a for…

A: Given that, f:A→B be a bijective function. We have to construct a function g:B→A such that gfa=a for…

Q: Let f: A -> B and g: B -> C be two functions. Prove: if f and g are surjective, then gof is…

A: Given: Let  f: A→B and g: B→C be two functions.  If f and g are Surjective(onto), To Prove:  g∘f:…

Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: (a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b)…

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Q: Let f be the function from {a, b, c, d} to {1, 2, 3, 4} with f(a) = 4, f(b) = 2, f(c) = 1, and f(d)…

A: For bijection, the function needs to be one to one and onto.

Q: Let f: X --> Y and g, h: Y --> Z be functions. Prove or disprove:  (a) If g of f is 1-1, then f is…

A: (a) Suppose g o f is 1-1. To prove f is 1-1.

Q: solve this question please:  Let X = {1, 2, 3}, Y = {1, 2, 3, 4}, and Z = {1, 2}:a. Define a…

A: The functions are as follows: a.f(1)=1f(2)=2f(3)=3. b.g(1)=1g(2)=2g(3)=1.Explanation:Steps and…

Q: Domain of F Co-domain of F X Y F a • d• Domain of G Co-domain of G X Y G a • b e of d• a. Is F…

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Q: Let A, B and C be nonempty sets and let f : A → B, g: BC and h: B → C be functions. For each of the…

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