Suppose functions w: PQ and h : Q+ R are both onto. Prove that the composite function is also onto.

Q: How many functions [5] to [3] are onto?

A: Solution

Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊mn ⌋.

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Q: Let f : R → R be f(r) = + 1+ \|° (a) Is ƒ everywhere defined? If not, give the domaim (b) Is ƒ onto?…

A: Given, f: R→R be                       f(x)=x1+|x|

Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. Is R reflexive?…

A: Given:  R is a relation defined on P 1, 2, … , 100 by A R B  if and only if A ∪ B is even. We have…

Q: Let ƒ : A → B be a function. Prove that f is onto if and only if there exists a function g : B → A…

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Q: Consider X = C[0, 1] with the norm = max |x(1)|, IE[0,1] and let T: X - X be the mapping given by…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Consider a relation R on Z defined as follows: xRy → xy is even. a. Give a counterexample to show…

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Q: Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it…

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Q: Give an example of onto but not 1-1 function f: 7⁰ → Z>⁰. tit 11-C.

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Q: Let T : V → U be a homomorphism, then Ker T = { 0 } iff T is one-one

A: A linear transformation is said to be injective or one to one if provided that for all v1 and v2 in…

Q: Let f :A→B and g : B +C be functions. Show that if g o f is onto, then g is onto.

A: Given: f:A→B and g:B→C are functions Given: gof: A→C is onto To show: g:B→C is onto That is,  for…

Q: Suppose f: A → B, f is one-to-one and onto, and Y c B. Show that the inverse image of Y under f and…

A: The function f is one-one and onto.   The function f is one-one if two different element in A…

Q: A function from ZxZ to Z defined by f(m, n) = m-n is an onto function. O True O False

A: The given function is                                     f: ℤ×ℤ→ℤ  such that    f(m,n)=m-n. A…

Q: f:A→Z is not onto and f:A M is onto.

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Q: Consider the relation S on N defined by uSy + 5|(y + u). Determine whether S is symmetric, reflexive…

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

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Q: Let L be the operator on P3 defined byL (p(x)) = xp'(x) + p''(x) If p(x) = a0 + a1x + a2(1 + x2),…

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Q: Let A be a finite set, and suppose that f : A → A is one-to-one. Does f necessarily have to be onto?…

A: The given question is solved below.

Q: Prove that for any set A, the identity function iA is a bijection.

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Q: 3. If f:(X,r)(Y.A) and g:(Y,A)→(Z,r) are open functions, prove that gof :(x.r)(Z.r) is open…

A: Definition: An open map is a function between two topological spaces that maps open sets to open…

Q: Give an explicit formula for a function from Z to Z+ that is a) onto, but not one-to-one. b)…

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Q: A function g: Z → Z is defined by the rule g(m,n)=m+n Determine whether it is onto or not...

A: Onto functions: A function f: A→B is said to be an onto function if range of function is equal to…

Q: If f, g E R[a,b] with f < g on [a,b], prove that g.

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Q: Prove that det(At) = det(A) for any A ϵ M2x2(F).

A: Suppose we are given a square matrix A with four-element: a,b,c,d A=abcdAt=acbd

Q: (b) Define the operator T: → as: (Tx) = for every x = () e t. That is, Tx = (61. for every x (f,E2.…

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Q: Let T be the linear thansformation from R5 to Rª defined by X1 1] X2 X1 1 3 2 X2 -8 1 -2 2 0 -1 4 X3…

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Q: (c) Suppose n = 5 and m = 4, determine the number of onto functions from A to B.

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Q: Suppose f : N→N and g :N→N , function f is not onto but f+g is onto function  does g onto function…

A: g is not necessary to be onto. See the attachment

Q: Prove: f € R(a) if and only if for each ɛ > 0, there exists a partition of [a, b ] , say go, such…

A: f∈Rα if and only if for each ε&gt;0,there exists a partition of a, b,say P, such that UP, f, α-LP,…

Q: Suppose  there exist transposition f_i , 1<=I<=t  such that

A:

Q: Let R be the relation defined on P({1,., 100}) by ARB if and only if |AU B| is even. s R reflexive?…

A: We will check one by one what properties R satisfies and which not.

Q: A relation R is defined on Z by xRy if x*y >= 0. Prove or disprove the following: a. R is…

A: Let us consider the given relation R on set X. R is said to be reflexive for any x in X, x R x. R…

Q: Prove that G and H IS sube GroP form CX H

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Q: Find examples of functions f and g such that f°g is a bijection, but g is not onto and f is not…

A: A function is said to be bijective if it is one-one and onto. We need to find f and g such that…

Q: Which of the following function f: Z XZ → Z is not onto? f(a, b) = a O f(a, b) = |b| f(a, b) = a - b…

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Q: 20. If f: X → Y and g: Y → Z are functions and gof is onto, must ƒ be onto? counterexample.

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Q: Prove or provide a counterexample to the following statement: if f : A → B and g : B → C are…

A: i have used the definition of onto functions and showed that c has no preimage under f  but gof is…

Q: or give a counterexample to the following stateme ons, then ƒ Ug is a function from DU B to C UA et…

A: Function is also a relation

Q: Given g, a function from A to B and f, a function from B to C. "If f and g are onto, then f • g is…

A: Given that g:A→B is onto. If y∈B, then there exists a pre-image x∈A. ⇒g(x)=y

Q: Prove or disprove For function f:→ R → R f(x) = x² and every onto function g(x) : [0, 00) → holds a)…

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

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Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊m/n ⌋

A: Given that: f(m,n)=mn,  f:Zx(Z-{0})→Z

Q: If V is finite dimensional ond f is a homomorphisni of V into itself which is not onto prove that…

A: If f is a homomorphism of V into itself, then f(0) = 0 .

Q: In this exercise, you want to show that a relation RC A? is transitive + R" C R for all n EN=…

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Q: Define a relation on Z by setting xRy if xy is even. a. Give a counterexample to show that R is not…

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Q: Suppose that o is differentiable. Prove the identity

A: follow next step

Q: 1. Check that the following functions on R² are norms: 1/p a) || (x1, #2) ||,= ( 1z1P + \zal" ) b)…

A: Given: a) x1, x2p=x1p+x2p1/p, 1≤p&lt;∞ b) x1, x2∞=max x1, x2 To check: Whether the given functions…

Q: Suppose f : N → N and g : N → N are functions such that f is not onto but f + g is onto. May we…

A: Given: Two functions f : N → N and g : N → N are functions such that f is not onto but f + g is…

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.