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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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do Exercise 17.1.15 part b and c

Hint for c: There are 9

We commonly use symbols such as =,<, C,... that are used to compare elements of a set. You may have called these "relations" in your high school 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 | x < y} (here the symbol ":=" means "defined as"). Note that R here is a subset of 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 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 Re 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 Rc associated with the symbol "C" applied to the subsets of A:= {1,2,3}. How many elements does Rċ have?
Transcribed Image Text:We commonly use symbols such as =,<, C,... that are used to compare elements of a set. You may have called these "relations" in your high school 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 | x < y} (here the symbol ":=" means "defined as"). Note that R here is a subset of 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 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 Re 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 Rc associated with the symbol "C" applied to the subsets of A:= {1,2,3}. How many elements does Rċ have?
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