a) For each of the following functions, identify 1) its image and whether it is 2)...
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a) For each of the following functions, identify 1) its image and whether it is 2) injective, 3) surjective, 4) bijective; if your answer is no, explain why. i) ƒ : R → R, ƒ(x) = 2l+0.5] ([x] is the biggest integer that is not larger than x). (5 Points) ii)f: Z→ ZxZ, f(n) = (n − 1, n+1). (5 Points) b) Let f: Nx N → N be a function defined as: Vn f(0, n) = n + 1 f(m, 0) = f(m-1, 1) Vm > 1 f(m, n) = f(m - 1, ƒ(m, n − 1)) Vm ≥ 1, n ≥ 1. Determine the value of f(2,3). (5 Points) c) Let A = {1,2,3,4} and B {4,5,6). Define a function f : P(A) × P(B) → P(AUB) by f((X,Y)) = XUY. Determine whether f is injective, surjective, or bijective. (10 Points) = a) For each of the following functions, identify 1) its image and whether it is 2) injective, 3) surjective, 4) bijective; if your answer is no, explain why. i) ƒ : R → R, ƒ(x) = 2l+0.5] ([x] is the biggest integer that is not larger than x). (5 Points) ii)f: Z→ ZxZ, f(n) = (n − 1, n+1). (5 Points) b) Let f: Nx N → N be a function defined as: Vn f(0, n) = n + 1 f(m, 0) = f(m-1, 1) Vm > 1 f(m, n) = f(m - 1, ƒ(m, n − 1)) Vm ≥ 1, n ≥ 1. Determine the value of f(2,3). (5 Points) c) Let A = {1,2,3,4} and B {4,5,6). Define a function f : P(A) × P(B) → P(AUB) by f((X,Y)) = XUY. Determine whether f is injective, surjective, or bijective. (10 Points) =
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Answer a i Function f RR fx 2x 05 Image The image of the function is the set of all possible outputs In this case the image is the set of all real numbers Injective A function is injective if each ele... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
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