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# Let f and g be functions from (1,. 2,. 3,. 4) to (a, b, c, ISBN: 9780073383095 37

## Solution for problem 13E Chapter 2.SE

Discrete Mathematics and Its Applications | 7th Edition

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Problem 13E

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, with f(1) = d. f(2) = c, f(3) = a. and f(4) = b, and g(a) = 2, g(b) = 1, g(c) = 3. and g(d) = 2.a) Is f one-to-one? Is g one-to-one?________________b) Is f onto? Is g onto?________________c) Does either f or g have an inverse? If so. find this inverse.

Step-by-Step Solution:

SolutionStep 1One to one FunctionA function is said to be one to one if every range of the function have exactly one domain of the function.Onto FunctionA function is said to be onto if every range of the function have at least one domain of the function.In the Question it is given that f(1) = d , f(2) = c , f(3) = a and f(4) = bNow we have to represent the function f maps A to B where A= {1, 2, 3, 4} be the domain and B = {a, b, c, d} be the range of the function. It is given that g(a) = 2 , g(b) = 1 , g(c) = 3 and g(d) = 2Secondly, we have to represent the function g maps B to A where where A= {1, 2, 3, 4} be the range and B = {a, b, c, d} be the domain of the function. Step 21. Yes, f be one to one function. No, g cannot be one to one function.1. No, f cannot be onto function.Yes, g be onto function.

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##### ISBN: 9780073383095

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