Explanation Approach: The two sets A and B are said to be equivalent when they have same cardinal number and represents as A ~ B . A one-to-one correspondence can be constructed between the elements of equivalent pair set only Calculation: The pair of set is written as, S = { 4 , 6 , 8 , ... , 664 , 666 } T = { 5, 6, 7, ... , 335, 336 } The set S contains even numbers from 4 to 666. So it is calculated as, n ( S ) = 666 2 − 1 = 332 The set T contains all natural numbers from 5 to 336. So it is calculated as, n ( T ) = 336 − 4 = 332 So, the sets have same cardinal numbers and hence are equivalent. Therefore, their elements can be put into one to one correspondence. A = { 4 , 6 , 8 , ... , 2 + 2 n ..

8th Edition

ISBN: 9781305104174

Author: David B. Johnson, Thomas A. Mowry

Publisher: Cengage Learning

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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

Chapter 2.5, Problem 10E

To determine

Whether the pair

S={4,6,8,...,664,666}T={5, 6, 7,..., 335, 336}

is equivalent or not and if they are equivalent then list one to one correspondence.

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Chapter 2.5, Problem 9E

Chapter 2.5, Problem 11E

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Whether the pair S = { 4 , 6 , 8 , ... , 664 , 666 } T = { 5, 6, 7, ... , 335, 336 } is equivalent or not and if they are equivalent then list one to one correspondence.

Solution Summary: The author explains that the two sets A and B are equivalent when they have the same cardinal number.

Concept explainers

Whether the pair

S={4,6,8,...,664,666}T={5, 6, 7,..., 335, 336}

is equivalent or not and if they are equivalent then list one to one correspondence.

Want to see the full answer?

Chapter 2 Solutions

Whether the pair S = { 4 , 6 , 8 , ... , 664 , 666 } T = { 5, 6, 7, ... , 335, 336 } is equivalent or not and if they are equivalent then list one to one correspondence.

Solution Summary: The author explains that the two sets A and B are equivalent when they have the same cardinal number.

Concept explainers

Whether the pair S={4,6,8,...,664,666}T={5, 6, 7,..., 335, 336} is equivalent or not and if they are equivalent then list one to one correspondence.

Want to see the full answer?

Chapter 2 Solutions

Whether the pair

S={4,6,8,...,664,666}T={5, 6, 7,..., 335, 336}

is equivalent or not and if they are equivalent then list one to one correspondence.