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 without justification. Also, produce an example of a function f : X → Y that is not onto.

Q: Let A, B, C be sets. Let f : A → B and g : B → C be functions. a) Prove that if f and g are…

A: We shall solve both parts of this question that you have posted.

Q: Let A and B are nonempty sets, and functionƒ maps A to B. Which of the sets below is the rang of the…

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Q: let P: XY be a function prove that Phas an inverse if and only if fis abijection.

A: Let us define a bijective functions. We know that , a function f : X → Y is bijective if it is both…

Q: Are the following functions 1-1, onto, both, or neither. f: R-R. f(x) = x13 h: Z- Z. h(x) = x g:…

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Q: Let A={a,b,c,d,e}. Find a relation R on A which is symmetric and transitive but not reflexive

A: Reflexive relation means every term of a set is related with itself

Q: Suppose that f is a function from A to B, where A and B are finite sets with |A| = |B|. Show that f…

A: Given that f is a function from A to B, where A and B are finite sets with A=B. We have to show that…

Q: 15. Determine whether the function f: Z x Z Z is onto if a) f(m, n) =m+n. b) f(m, n) = m² + n². c)…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Let f: X → Y and define x~y if f (x) = f (y). Show that - is an equivalence relation on X.

A: The objective is to show that ~ is an equivalence relation on X.

Q: 1. Let X = {m, a, t, h}, Y = {1,4, 0}, Z = {d,i, s, c, r, e,t, e} (a) Define a function f : X →Y…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Let X= {p, q, r, s, t}, Y= {1, 23} and Z={k, e} Define one-to-one function and how many one-to-one…

A: Given X= {p, q, r, s, t}, Y= {1, 23} Z={k, e}

Q: Prove the following statements a. Let X and Y be nonempty sets and f: X→Y. If A⊆X and B⊆Y, then…

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Q: Let ƒ be a mapping from [2, +∞ [to, +∞[defined by: 3 f(x) = x + = x f has a fixed point. O False O…

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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: Which of the following function f: Z x Z Z is not onto? 2020 a. f(a, b) = a b. f(a, b) = lbl c. f(a,…

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Q: Let Z be the set of integers and f:Z Z be defined as f(x)=-2x-3. Then the inverse function of exists…

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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: Let A and B be sets and f a function from A to B. Then the following assertions hold: f'is onto if…

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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: Exercise 2.12. Determine whether or not the given functions f:Z Z are one-to-one or onto (or neither…

A: The solution of given functions is given as follows :

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: 4. Let X be any finite set and define the relation R on P(X) by R= {(E,F)||E| = |F\, E, F € P(X)}.

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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: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Let R be a relation on the set of all functions from Z to Z defined by: R = {(f,9)|f(1) = g(3) or…

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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: Let V={1,2,3,4} and W={a,b,c}. Function f:V → W is defined as follows: (c) f(1) = c,f(2) = a, f(3) =…

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Q: Every injective function is onto. True False

A: Answer and explanation is given..

Q: Show that if f and g are continuous on [a, b] and if f(a) g (b), then there exists some ce ]a, b[…

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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: Let f : A → B and g : B C be surjective functions. Prove or disprove whether gof is surjective.

A: Here given that                       f :A→B   and    g :B→C  be both surjective function .  Now we…

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: 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: Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions…

A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

Q: (ii) Let A be a non-empty set and f: AA be a function. Prove that if fof is injective, then / is

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Q: Let g: A ---------- B andf: B-----------C. Prove that f is onto if f 0 g is onto.

A: Given:g:A→B;     f:B→CTo Check : if (f∘g):A→C then f is ontoNow given…

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: 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: Let A and B be sets. Show that               f : A × B → B × A such that                  f(a, b) =…

A: Given:

Q: Is the function f(x) = x2 from the set of integers to the set of integers onto?

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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: Let A be a nonempty set and let f : A → B be a function. Prove that f is one-to-one if and only if…

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Q: Let z be the set of integers and f:Z → Z be defined as f(x)=-4x+5. Then the inverse function of f *…

A: We know that inverse of a function exist if it is has one to one correspondence and it is onto. If…

Q: Let X, Y be nonempty sets. Let A, B c X and P, Q C Y. Let f:X → Y be a function. Prove or give…

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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: 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: 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: Let function f:Z Z be defined as follows; x– 1 x is odd f(x) = < (x² + 2 x is even The function f is…

A: Let, x=2 that is x is even. Then, fx=x2+2 So, f2=22+2=6f-2=-22+2=6 Therefore, f2=f-2 Then, the given…