true or false? PROVE YOUR ANSWER b) If f :N→N and g :N→N are functions such that f is not onto but  fg is onto, then g is onto. The claim is of answer:                           prove of answer

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Q: Let f: R→R be the function defined by f(x)=17x+3.    a) Is f is one-to-one? If yes, then explain…

A: Let f: R→R be the function defined by f(x)=17x+3.  a) Is f is one-to-one? If yes, then explain why.…

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Q: 6. For nonempty sets A, and B. let f: A→A and g: A → B be functions. Prove if the statements that…

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Q: Suppose f X→ Y, and A, B C X. Prove that (a) f(AUB) = ƒ(A) U ƒ(B) (b) ƒ(ANB) ≤ ƒ(A) Ñ ƒ(B)

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Q: How many functions f: {1,2,3,4} {1,2,3,4} are there satisfying: a. f(1) = 1 or f(2)= 2 (or both)? b.…

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Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

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Q: True or False: ⊨ F ⊃ T ⊨ - means logically valid , F-false, T-true

A: We know,       A ⊃ B is equivalent to ~A v B

Q: Let f, g,h: A→ A be any bijective functions. Then (f ogoh)-

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Q: Consider the function g : Z × Z → Z defined g(x, y) = |x| − |y|, prove if it is onto or not? Is it…

A: Given function is g:Z×Z---&gt;Z  defined by g(x,y)=|x|-|y| the function is one one if every…

Q: one-to-one

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Q: Exercise 5.96. Give an example of each of the following and give an informal proof of the properties…

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Q: (b) ƒ(AnB) ≤ f(A) Ñ ƒ(B)

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Q: Consider the functions f : R R and g : R → R defined so that f(x) = x and g(x) -2x = e for all x E…

A: Given f(x) = x3 g(x) = e-2x

Q: (a) Define a function f: N→ N that is one-to-one but not onto. (b) Define a function f: N→ N that is…

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Q: true or False? Prove your answer!  a) Suppose h:R→R is not one-to-one, and suppose a, b∈R with a≠b.…

A: (a) The given statement, "Suppose h:R→R is not one-to-one, and suppose a, b∈R with a≠b then h(a)…

Q: Prove: There exist functions f, g, h in F such that g o f = h o f, but g is not equal to h.

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

Q: How many functions f: {1,2,3,4} → a. ƒ(1) = 1 or ƒ(2) = 2 (or both)? → {1, 2, 3, 4} are there…

A: Since your question carry more than three subparts , so as per Bartleby guidelines we are answering…

Q: Prove that n is odd if and only if 3n+9 is even. You must use definitions of even (and odd, if…

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Q: Let f : X → Y and g : Y → Z be functions such that h = go ƒ is a one-to-one correspondence. (a)…

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Q: Let f : Z → Z be relation defined by f(x) = ||æ| – 5|+ x for all æ E Z. i) f is a function ii) f is…

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

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Q: Define g: (-0, ∞) → [-1,1] by f(x) = sin x ,Vx E R. This function is onto. %3D

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Q: Which functions are one-to-one? Which functions are onto? Describe the inverse function for any…

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Q: Exercise 4.4.5. Let A and B be sets. Prove that there is a bijective function f: A × B → BXA.

A: A and B are two sets.  We need to prove there is a bijective function            f : A × B → B × A.

Q: Prove: If f₁, f₂ € R(a) on [a, b] with f₁ ≤ f₂, then so f₁ da ≤ f f₂ da.

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Q: Let N be a relation on R where xNy if and only if xy < 0. Is N reflexive? Is N symmetric? Is N…

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Q: Let f:Z → Z be given by f (x) = 3x + 1. a. Show that f is one-to-one. 7. b. Is f onto? EXPLAIN.

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Q: Let f = u + iv be analytic in the connected open set and assume u and v satisfy u? + 3v2 = 4. Show f…

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Q: Let G be the interval (-3/2, ∞). Let □ be the operation on G such that, for all x, y € G, xay=2xy…

A: Introduction: In mathematics, an identity is a relationship between two mathematical expressions A…