Determine whether each of the following statements is true or false. a. xe {x} ( Because x is the member of the singleton set { x } ) b.{x}c {x} ( Because Every set is the subset of itself. Note that every Set has necessarily two subsets Ø and the Set itself, these tv subset are known as Improper subsets and any other subset is called Proper Subset) c.{x} e {x} ( Because { x} is not the member of {x} ) Similarly other {x} € {{x}} TRUE TRUE FALSE d. TRUE Øc {x} TRUE е. f. Øe {x} FALSE

Determine whether each of the following statements is true or false. a. xe {x} ( Because x is the member of the singleton set { x } ) b.{x}c {x} ( Because Every set is the subset of itself. Note that every Set has necessarily two subsets Ø and the Set itself, these tv subset are known as Improper subsets and any other subset is called Proper Subset) c.{x} e {x} ( Because { x} is not the member of {x} ) Similarly other {x} € {{x}} TRUE TRUE FALSE d. TRUE Øc {x} TRUE е. f. Øe {x} FALSE

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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Concept explainers

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.

Question

Determine whether each of the following statements is true or false.
a. xe {x}
( Because x is the member of the singleton set { x } )
b.{x}c {x}
( Because Every set is the subset of itself.
Note that every Set has necessarily two subsets Ø and the Set itself, these tw
subset are known as Improper subsets and any other subset is called Proper
Subset)
c.{x} e {x}
( Because { x} is not the member of {x} ) Similarly other
{x} e {{x}}
Øc {x}
Øe {x}
TRUE
TRUE
FALSE
d.
TRUE
е.
TRUE
f.
FALSE

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