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 onto." O False O True
Q: (c) Show that if g o f is onto then g must be onto.
A: Solution:-
Q: 6. Show that if f : X Y and g : Y → Z are both onto then fg : Z -→ Z is onto. (Note this is function…
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Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊mn ⌋.
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Q: Suppose f: A g(b)= {a E A | f(a) =b}. Prove that if f is onto then g is one-to-one. What if f is not…
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Q: Let A and B be two sets with |A|| = n and |B|| m, where n and m are positive integers. Answer each…
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Q: The context for this problem is as follows: g is a function from X to Y and f is a function from Y…
A: Let, a,b→x,y contains a,x,b,y and gx,y,c→w,z be function contains c,w,x,z,y,z
Q: Let z be the set of integers and f:Z→Z be de fined as f(x) =-7x+2. Then the inverse function of f *…
A: Does not exists because f is not onto.
Q: Let ƒ and g be functions from {1,2,3,4} to {a,b,c,d} and fro {a,b,c,d} to {1,2,3,4}, respectively,…
A: The function f is onto if and only if for every element b∈B there exist an element a ∈A such that…
Q: Define a relation D on the set of real of numbers as follows: Vx, y ≤ R, x Dy x-y is irrational OD…
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Q: Let A and B be subsets of the set S, where |S| = 10 and |B| = 5. Let ƒ : A → B be a function. (a) If…
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Q: If for each element y in Set B there exists an element x in Set A such that f(x) = y, then the…
A: A function f : A → B is said to be (a) one to one function - If the images of distinct elements of…
Q: Suppose that the function b satisfies the necessary Rolle's theorem in [-3, 1], then the value of q…
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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: Given that f is a function from A onto B, that g :B →C, and that the function g • f is one-one,…
A: In the given question we have to find f and g are one - one function.
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: 5. Determine whether the function f : Z × Z →Z is onto if a) f (m, n) = m² + n² b)f (m, n) = m³
A: See the solution.
Q: A function f() from {a, b, c, d} to { 1, 2, 3, 4} defined by f(a) = 3, f(b) = 2 and f(c) = 1 and…
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Q: Give a proof of the following statement. Suppose A, B and C are sets, f is a surjective function…
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Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f: X → Y can be one-to-one or not…
A: By using definition of one-time and onto function we solve the given problem :
Q: 5. Given a function f: A → B. Define the relation f from P(A) to P(B) by f = {(X,Y)C P(A) × P(B) | Y…
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Q: A relation \(R\) on a set \(AV) is called anti-symmetric if O (a.b) \in R\) implies ( (b,a) \in R\)…
A: Anti symmetric relation is as follows: If (a, b) and (b,a) lies in R then must be a=b.
Q: Every injective function is onto. True False
A: Answer and explanation is given..
Q: Suppose f: A→ B and g: B→ C are functions, show that a) If both f and g are one-to-one, then go f is…
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Q: 7. Find a counterexample or a proof for the following statement: If f: A- B and g : B- C are…
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Q: a. The function f : Z → Z, f(x) = 2x is onto. (A) True (В) False b. The function f : Z → Z, f(x) =…
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Q: All but two of the following statements are correct ways to express the fact that a function f is…
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Q: Let X = {1,2,3,4} and Y = {5,6,7}. State whether a function f : X → Y can be one-to-one or not…
A: By using definition of one-time and onto function we solve the given problem :
Q: 7. If a functionf defined in [a, b] is such that o (i) f is derivable in [a, b], (ii) f' (a) and f'…
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Q: Suppose f: A --> B is a function and g is the powerset of B to the powerset of A, while g(S) =…
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Q: Supposef:N→N and g:N→N are functions such that f is not onto but f+g is onto. May we conclude that g…
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Q: Suppose f : N → N is an injective function on the natural numbers which, considered as a relation,…
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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: Given f: {0, 1, 2,...} → R and f(x) = x, then O f(x) is a one-to-one (injective) function. O All of…
A: We have to find out the solution
Q: Which one of the following statements is a true statement? O If f:A » B and g:B → C are functions…
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Q: Suppose that g is a function from A to B and f is a function from B to C. Prove each of these…
A: The solution is given as
Q: Given. f: {a, b, c, d} to itself f(a) = d, f(c) = a, f(a) = b, f(d) = c, f(b) = a Which of the…
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Q: 1. Give an example of a function that is one-to-one but not onto. Give an example of a function that…
A: An example of a function that is one to one but not onto b) an function that is not one to one but…
Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…
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Q: 7. Let A and B be sets, and let f: A → B and g: B → A be functions. Suppose that: • go f(a) = a for…
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Q: Let f and g be functions from {1,2,3,4} to {a,b,c,d} and from {a,b,c,d} to {1,2,3,4}, respectively,…
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Q: Let R be a relation from A to B and S a relation from B to A. Prove or disprove that if S of R =…
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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: If B is countable and f : P(A) → B is a one to one (i.e., injective) function, then A must be…
A: We have to find is the statement is true or false.
Q: Let A and B be nonempty sets. Prove the following statements. (a) For any function f:A→A, if f◦f is…
A: (a) Let z be an element of A. Since fof is onto there is an element x in A such that fof(x)=z.…
Q: Suppose functions w: PQ and h : Q+ R are both onto. Prove that the composite function is also onto.
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Q: (d) Give an example of functions f: A → B and g: B → C, such that go f is onto, but ƒ is not onto.…
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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…
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Solved in 2 steps
- Give an example of mappings and such that one of or is not onto but is onto.Let a and b be constant integers with a0, and let the mapping f:ZZ be defined by f(x)=ax+b. Prove that f is one-to-one. Prove that f is onto if and only if a=1 or a=1.Label each of the following statements as either true or false. Let f:AB where A and B are nonempty. Then f1(f(T))=T for every subset T of B.
- True or False Label each of the following statements as either true or false. Let and such that is onto. Then both and are onto.Label each of the following statements as either true or false. 3. Let where A and B are nonempty. Then for every subset S of A.Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every subset T of A.