Please do Exercise 17.1.15 part b and cHint for c: There are 9 We commonly use symbols such as =,<, C,... that are used to compareelements of a set. You may have called these "relations" in your high schoolalgebra class and in fact, they can all be considered as binary relationsin the sense of Definition 17.1.2. For example, using the symbol < we candefine the following binary relation on R:R<= {(x, y) = R XR | x < y}(here the symbol ":=" means "defined as"). Note that R here is a subsetof R x R, so it is indeed a binary relation according to Definition 17.1.2.Exercise 17.1.15.(a) Define the set R associated with the symbol ">" applied to the naturalnumbers.(b) Define the set R associated with the symbol "=" applied to the com-plex numbers. In your definition assume that equality of real numbershas been defined, and write complex numbers in rectangular form (forexample, a + bi or c + di).(c) List all the elements of the set Re associated with the symbol "C"applied to the subsets of A := {1,2}. (The set of subsets of A is denotedas P(A), the power set of A.) (*Hint*)(d) Consider the set Rc associated with the symbol "C" applied to thesubsets of A:= {1,2,3}. How many elements does Rċ have?

algebra class - and in fact, they can all be considered as binary relations in the sense of Definition 17.1.2. For example, using the symbol < we can define the following binary relation on R: R<= {(x, y) = R XR|r" applied to the natural numbers. (b) Define the set R associated with the symbol "=" applied to the com- plex numbers. In your definition assume that equality of real numbers has been defined, and write complex numbers in rectangular form (for example, a + bi or c+di). (c) List all the elements of the set R associated with the symbol "C" applied to the subsets of A:= {1,2}. (The set of subsets of A is denoted as P(A), the power set of A.) (*Hint*) (d) Consider the set R associated with the symbol "C" applied to the subsets of A := {1,2,3}. How many elements does R have?

algebra class - and in fact, they can all be considered as binary relations in the sense of Definition 17.1.2. For example, using the symbol < we can define the following binary relation on R: R<= {(x, y) = R XR|r" applied to the natural numbers. (b) Define the set R associated with the symbol "=" applied to the com- plex numbers. In your definition assume that equality of real numbers has been defined, and write complex numbers in rectangular form (for example, a + bi or c+di). (c) List all the elements of the set R associated with the symbol "C" applied to the subsets of A:= {1,2}. (The set of subsets of A is denoted as P(A), the power set of A.) (Hint) (d) Consider the set R associated with the symbol "C" applied to the subsets of A := {1,2,3}. How many elements does R have?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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