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 function are there from to Define onto function and how many onto function are there from to.

Q: A of A is a function from A to A that is both one-to-one and onto.

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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: 1. Let A = {a, b, c}, B = {1,2,3}, C = {x, y, z, w}, D = {4,5, 6}. Let the functions f : A → B, g :…

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Q: Answer with True or False. 1. The functions from Z to Z is onto if f(n)=n−1. 2. These function…

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Q: Theorem 4. Let X be a set, and let F: X Y be a l-1 and onto function. (a) F-lo F = Idx (b) FoF- =…

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Q: Consider the functions, f:A → B and g:B→ A on the sets A={1,2.3,4,5), B=(3,6,9.12} given by…

A: According to question We have to calculate for the given function sets.

Q: Let f, g be two functions from a set A to itself. If f o g is surjective, does it imply that g o f…

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Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (x, y) and (z, w) in A, (x, y)R(z, w)…

A: We will find out the required values.

Q: Let A = {x, y} and let S be the set of all strings over A. Define a relation C from S to S as…

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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 A = {1,2,3,4,5,6} and R a relation on A whose MR is given below 0 100 0 1 0 0 1000 10 0 10 1 0…

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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: 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: 2. Determine whether each of these functions from {a,b,c,d} to itself is one-to-one. a. f(a)=b,…

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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: Let A = {1, 3, 5, 7, 9, 11}, B= {a, b, c, d, e}, and ƒ be the function from A to B defined as below:…

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Q: Let A = (1, 2, 3, 4, 5) and B = {a, b, c) and f = {(1, a), (2, a), (3, b), (4, b). (5, b)}. Choose…

A: Given. (a) f is a onto function because image of 1 and 2 are same also image of 3, 4 , 5 is same.…

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

A: To show that  a function f(x) is one-one , we have to show that for all x , y belong to the given…

Q: (a) f is a one-to-one function (Type Y for "yes" or N for "no") (b) ƒ is an onto function (Type Y…

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Q: Prove a Function is Onto Use the definition of onto to prove that the given function is onto. Let…

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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: 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 G = {-2,0, 2} and H = {4,6,8} and define a relation V from G to H as follows: %3D For all (x, y)…

A: Solve the following

Q: A relation R on a set A is defined to be irreflexive if, and only if, for every x E A, x R x;…

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Q: 1. Show that which of these relations on the set of all functions on Z-→Z are equivalence relations?…

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Q: (a) Prove that there exists a function f : Z → Z so that f is one-to-one but f is not onto. (b)…

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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: Let, X, Y, Z be sets of sizes x, y and z respectively. Let W = Xx Y and E be the set of all subsets…

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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: Let G = {-2, 0, 2} and H = {4, 6, 8} and define a relation V from G to H as follows. For every (x,…

A: Given,            G=-2, 0, 2  and   H=4, 6, 8and  define a relation v from G to H as follows.For…

Q: Prove the theorem: For finite sets X and Y, let |X|=m and |Y|=n. If there is an onto function f:X →…

A: please see the next step for solution

Q: 2. Let X and X, be sets. Define functions T1 : X1 x X2 → X1, T2 : X1 × X2 → X2 by T1(X1, X2) = X1,…

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Q: Let f: X→Y be a surjective function. Define a relation on X by setting ay iff f(x) = f(y). Let E be…

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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: Let N be endowed with the discrete topology and Y= {0}U nEN-{0,1} be a subespace of R. The topology…

A: Que 1 From the given information. Y is a subspace of R and it is defined as follows. The function f…

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

A: One to one function: Let us define a function f:A→B is said to be one to one function if…

Q: 1*) Let X = {1,2, 3}, Y = {2,3, 4}, and Z = {1,2}. (a) Define a function f: Z → X that is one-to-one…

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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: 2. Let X be an uncountable set and let Y be a countable set. (a) If f : X → Y is a function, prove…

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Q: Let A be a nonempty set and let P be a partition of A. Define a relation R (corresponding to P) on A…

A: Given, A=1,2,3 We can write the above set as, 1,2,3×1,2,3=1,1,,1,2,1,3,2,1,2,2,2,3,3,1,3,2,3,3

Q: Show that a one-one function                 f : {1, 2, 3} → {1, 2, 3} must be onto.

A: Given, the function f : {1, 2, 3} → {1, 2, 3} is one-one.

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…

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…

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Q: Determine whether the following relation is a function from R into R. A Iso deter- mine whether that…

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Q: 12. Prove the theorem: For finite sets X and Y, let |X|=m and |Y|=n. If there is an onto function…

A: Given below the detailed solution

Q: Let A = Z+ x Z+. Define a relation R on A as follows: For all (r, y) and (z, w) in A, (x, y)R(z,w) +…

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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…