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. Fill in the blank with “all", “no", or “some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is “all", then give a brief explanation as to why. • If your answer is “no", then give an example and a brief explanation as to why. • If your answer is “some", then give two specific examples that illustrate why your answer

. Fill in the blank with “all", “no", or “some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is “all", then give a brief explanation as to why. • If your answer is “no", then give an example and a brief explanation as to why. • If your answer is “some", then give two specific examples that illustrate why your answer

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.3: Divisibility
Problem 10TFE
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Fill in the blank with “all”, “no”, or “some” to make the following statements true. Notethat “some” means one or more instances, but not all.

5. Fill in the blank with "all", “no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is “all", then give a brief explanation as to why. • If your answer is “no", then give an example and a brief explanation as to why. • If your answer is “some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. An example must include either a graph or a specific function. f(x) is defined but not differentiable at r = 1, then g(x) (а) For functions f and g, if either f(x) or g(x) is not differentiable at r = 1. (b) For defined, then (f -g)" = f - g" + f" - g. functions f and g, if ƒ and g are two functions whose second derivatives are (c) For functions f and g, (f(x)·g(x))' = f'(x) · g'(x). In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the "if" part of the statement is true, but the “then" part of the statement is false.
Transcribed Image Text:5. Fill in the blank with "all", “no", or "some" to make the following statements true. Note that "some" means one or more instances, but not all. • If your answer is “all", then give a brief explanation as to why. • If your answer is “no", then give an example and a brief explanation as to why. • If your answer is “some", then give two specific examples that illustrate why your answer it not "all" or "no". Be sure to explain your two examples. An example must include either a graph or a specific function. f(x) is defined but not differentiable at r = 1, then g(x) (а) For functions f and g, if either f(x) or g(x) is not differentiable at r = 1. (b) For defined, then (f -g)" = f - g" + f" - g. functions f and g, if ƒ and g are two functions whose second derivatives are (c) For functions f and g, (f(x)·g(x))' = f'(x) · g'(x). In mathematics, we consider a statement to be false if we can find any examples where the statement is not true. We refer to these examples as counterexamples. Note that a counterexample is an example for which the "if" part of the statement is true, but the “then" part of the statement is false.
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