Z is the set of integers, R is the set of real numbers. 2) For each of the following functions prove whether they are i) one to one;   ii) onto. If they are not one to one or onto, show why. a) f: Z -> Z, f(n) = n - 6; b) f: Z -> Z, f(n) = n3; c) f: Z -> Z, f(n) = n2 + n;

Q: Let A, B, C denote sets. Let g, h : A → B and f : B → C denote functions. Assume f is one-to-one and…

A:

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

A:

Q: Consider a ruler that takes as input any integer z and outputs. Is r a function? Why?

A: Given that r takes input as integer z and outputs Here the input is different while the output is…

Q: Which of the following two-digit internal operations on the set of all real functions is not…

A: The given operations are

Q: ›) Prove that if the function ƒ is 1-1, then ƒ−¹ is a function. Caution! The ONLY assumptions here…

A: We use definition of function and one-one function to prove that f-1 is function.

Q: suppose g: A---> B and f: B---> C  are both one-to-one. prove f o g is one-to-one

A:

Q: d) Let the set A = {1, 2, 3,4} and let P(A) denote the power-set of A. Consider the following…

A:

Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: Let The the domain of f is the set of all real numbers except Number Moreover, f (2) f(t+1) = Number…

A:

Q: Q1. Let f: X-Y and g: Y - Z be two functions then a. If gof: X-Z bijective function then / and g are…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let f: A -> B and g: B -> C be two functions. Prove: if f and g are surjective, then gof is…

A: Given: Let  f: A→B and g: B→C be two functions.  If f and g are Surjective(onto), To Prove:  g∘f:…

Q: Count the number X of functions y: (20, 21,..., 23) → (5,6,...,8) so that is not onto. X =

A: Given function φ:(20,21,...,23)→(5,6,...,8)

Q: Let S be the set of all strings of a's and b's of length 3. Let B = {0, 1}. Let f: S B be defined as…

A: S be the set of all strings of a's and b's of length 3 . Then to find f(aaa) , f(aab) , list all the…

Q: 5. (8 points) Let S4be the set of all strings of 0's and 1's of length 4. Define F:S4 → Znonneg such…

A: The objective of the question is to understand the properties of the function F defined on the set…

Q: --to-one o? [ Se

A:

Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: Consider the set N²= NX N, the set of all ordered pairs (a, b) where a and b are natural numbers.…

A:

Q: Which of the following relations is not a function? a) b) V c) d)

A: To check whether the graph of a given relation is a function or not,we draw vertical lines which are…