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 following, prove or disprove: (a) If f is bijective and go f = hof, then g = h. (b) If gof=hof, then g = h.

Q: Label each of the following statements as either true or false. Let g: A ------- B and f: B…

A: g: A ------- B and, f: B --------C  f 0 g is one-to-one

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A:

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A: We have to check

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A:

Q: a. Find all relations from {a. b. c} to {u, v} b. Find all functions from {a. b. c} to {u, v} c.…

A: Let us take A= {a,b,c} and B={u,v}

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A: Given, A=1, 2, 3B=0, 1, 2

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A: The solution is given as

Q: Let A={2,4,6 } and B={1,3,5,}. which of the relations, R,S,and T defined below are functions from A…

A: We know that relation is said to be a function if every element in the domain have exactly one value…

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: 1. Is the relation { (0,0), (1,1), (2, 4), (3, 9), ... (n, n²).….}? Givon

A: 1 Given relation is 0,0,1,1,2,4,3,9,.......n,n2. We have to check that whether the given relation is…

Q: Let A = {d, e, f} and B = {0, 1} Define a relation as follows: ARB = {(d, 1), (f,0)} Select the…

A:

Q: . Determine if y is a function of x in x = y? + 5.

A: Given equation - x = y2+5Let's solve for y =- y2 = x-5y = x-5       ........(1)

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Q: 1. Consider the functions f : A → B and g : B → C. a. If f and g are both injective, show that so is…

A:

Q: C = {4x + 1] x € Z+}, D = {c + d]c € C, d € C}, E = C × D Is C a subset of D or E? Explain a…

A:

Q: 2. A function, f, is called ....if, whenever a + b, then f (a) + f (b). That is, for any two…

A: Here if a≠b then f(a)≠f(b) is equivalent as f(a)=f(b) then a=b

Q: Given x = {5,10,15,20,25,30} and y function from X to Y. Let f(5) = 400, f(10) = 100, f(15) = 500, f…

A: x=5, 10, 15, 20, 25, 30  &  y=100, 200, 300, 400, 500, 600. f5=400,  f10=100,  f15=500,…

Q: What is the correct aanswer

A: Topic:- function

Q: . For nonempty sets A, B and C, let f : A → B and g: B → C be functions. (a) Prove: If g of is…

A:

Q: . Determine whether the relation represents y as a function of x. T 4 4 14 2 -13 0. 4 25 A) Function…

A: Consider the provided table, We have to determine whether y is a function of x or not.