18. Specify a codomain for each of the functions in Exercise 16. Under what conditions is each of these functions with the codomain you specified onto?

Q: (c) Show that if g o f is onto then g must be onto.

A: Solution:-

Q: 1.4.10. Prove that the closed interval [0, 1] and the open interval (0,1) have the same cardinality…

A: (Schr¨oder-Bernstein theorem) :Let A and B be sets. Suppose there are injective functions f : A → B…

Q: Prove by bijective (one to one onto) of function 2" f: 2ln] P(({0, 1}, n)).

A: In this question we have to deal with the cardinality of a function.

Q: Let T = {x, y}. List all the strings of length 5 over T that have exactly one y.

A:

Q: A mapping is onto if and only if its codomain and rangear e equal.

A: Onto function: A function f:A→B is called a "surjective" or "onto" if the range of function is equal…

Q: Let A be the set of all 50 students of Class X in a school. Let f : A → N befunction defined by f(x)…

A: Given, Let A be the set of all 50 students of Class X in a school. Let f : A → N be function defined…

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A: GivenIf a nonempty set S contains an upper bound, then a least upper bound must exist in S.

Q: Suppose A and B are both countably infinite sets. Show that the union of A and B is also countably…

A:

Q: Show that an onto function f :               {1, 2, 3} → {1, 2, 3} is always one-one.

A: Given, f :  {1, 2, 3} → {1, 2, 3}  is an onto function.

Q: (c).Prove that set of real numbers E is closed and bounded if and only if every infnite subset of EE…

A: According to the given information, it is required to prove that:

Q: Let G be a a gsoup psove that CGIG)-1and (G:le))-IGI-

A:

Q: 8. Prove the idempotent laws in Table 1 by showing that a) AUA = A. b) ANA= A. %3D 9. Prove the…

A: Let's find.

Q: Suppose the set of natural numbers is constructed by the constant 0 and the successor function s.…

A:

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

A:

Q: Consider the functi on f(z) = 2 -a with lal >1 %3D 1- az Show that if 121 >1, the lf(Z)< 1

A: Given the function f(z)=z-a1-a¯z with |a|&gt;1.To prove that if |z|&gt;1, then |f(z)|&lt;1

Q: Suppose that N+ 1 balls, of which a+b+1 are red and N-a-bare blue, are arranged in a linear order in…

A: From the given information, There are N+1 balls, of which a+b+1 are red and N-a-b are blue arranged…

Q: Show {5, 10, 15, 20, - - ·} is countable. (Hint: Use the function f(n) and onto). = 5n and show it…

A: 4 Given set is 5,10,15,20,....... We have to show that the set 5,10,15,20,...... is countable. Let a…

Q: Exercise 6.40. Let E be a nonempty subset of R that is bounded above. Prove that if a = sup E, then…

A: This is the question of topology.

Q: Label each of the following statements as either true or false.   Every upper bound of a nonempty…

A: Consider the given information. According to the definition of upper bound, if F is an ordered field…

Q: 1. Find all 4 second-order one-way speech numbers of the following function. 2. Find using the…

A:

Q: 5. Construct a smallest binary relation S defined on the set {w,r, y, z} such that S satisfies all…

A: Consider the set, A=w,x,y,z, where all the 4 elements are distinct.

Q: Now let G = S_10, acting on the set {1,2,3,4,5,6,7,8,9,10}. What is the index in G of the stabilizer…

A:

Q: (b) If P is the projection on ce M of a Hilbert space H th riant under an operator T

A:

Q: Prove that |[0, 2]| = |(3,6)|. Make sure to prove that your functions are well-defined (that they…

A:

Q: A relation R defined on the given set A will satisfy

A:

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

A:

Q: QUESTION 3 Define: Onto (as it applies to functions on sets)

A: We have to define an onto function. For this, first we will provide the definition of a function in…

Q: Let ƒ (x)

A: Consider the function fx=1x+1xx−1 Simplify it fx=1x+1xx−1=x−1+1xx−1=xxx−1=1x−1 Hence, fx=1x−1

Q: Every injective function is onto. True False

A: Answer and explanation is given..

Q: 5. Show that the set {e" : n e Z} is countable. (Hint: Use the function f(n) = en and show it is 1-1…

A:

Q: Let F subseteq K be a Galois extension with Col

A:

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

A:

Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

Q: Suppose that operatorậ & ậ* in H= hw. (a*3 +) obeys anticommutation relation {ậ, ậ*} = ậa* + â*â = 1

A:

Q: Prove that if a is an upper bound for A, and if a is also anelement of A, then it must be that a =…

A: We have to prove that if a is an upper bound for A, and if a is also an element of A, then it must…

Q: Prove that if A ⊆ B and both sets have minima then min B ≤ min A

A:

Q: (a) Consider the customers with IDs ranging from p to q, inclusive, where p< q and consider the…

A:

Q: Find an example of on a set X (G has or H of G which has le

A: Given: that Group G is active transitively on set X . G has only one orbit and subgroup H of G has…

Q: in extension of a fie elements in K which ver F from a subfie

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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.

A:

Q: Let S be a subset of a Hilbert space H. Show that S- = s+.

A:

Q: Determine whether the function f: Z x Z -→ Z is onto if f (m, n) = .m + n

A: We will solve the problem using the definition of onto function.

Q: ntin

A: It is given that,  If g is continuous and ∫-28g(x)dx=30 We have to find ∫-144g(2x)dx=?

Q: Drag the correct description of the transformation and congruence criterion into the empty box below…

A: Given,

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

A:

Q: 1. If f:X → Y and g:Y → Z are functions and gof is onto. a. Must g be onto? Give a proof or a…

A: (a) Given that  f:X→Yg:Y→Z and g∘f is onto To prove : g is onto Let x∈X, y∈Y , z∈Z As gof is onto…

Q: Consider f : X →Y, with domain X = {c,j,v, m, e, s, n, q, u, d, i, g} and codomain Y = {80,08, 57,…

A: SOLUTION-

Q: 14,497 where y is the 55000 and older with at least a indicates a linear relation nt of 0.7581.…

A: Note:As per the requirement of the students solving part(c). Let Y= a+bX be the regression line.…

Q: (8) A space X is connected space IFF every continuous funetion f:X → D, Where D-(0,1} with discrete…

A: a) Constant function