a.
Find the cardinality
a.
Answer to Problem 2E
Explanation of Solution
Given information:
Calculation:
Here we will consider the following set:
Now, suppose
As the number of elements in set
Thus, cardinality of
Now, define a function
Now, we prove that
Thus,
Now, to prove that
Let
Let
Thus, for
Thus,
Hence, there is one-to-one correspondence from set
b.
Find the cardinality
b.
Answer to Problem 2E
Explanation of Solution
Given information:
Calculation:
Here we will consider the following set:
Now, suppose
As,
Thus,
As the number of elements in set
Thus, cardinality of
Now, define a function
Now, we prove that
Thus,
Now, to prove that
Let
Let
Thus, for
Thus,
Hence, there is one-to-one correspondence from set
c.
Find the cardinality
c.
Answer to Problem 2E
Explanation of Solution
Given information:
Calculation:
Here we will consider the following set:
Now, suppose
As,
Thus,
As the number of elements in set
Thus, cardinality of
Now, define a function
Now, we prove that
Thus,
Now, to prove that
Let
Let
Thus, for
Thus,
Hence, there is one-to-one correspondence from set
d.
Find the cardinality
d.
Answer to Problem 2E
Explanation of Solution
Given information:
Calculation:
Here we will consider the following set:
Now, suppose
As,
Thus,
As the number of elements in set
Thus, cardinality of
Now, pairing of
Hence, this pattern defines one-to-one correspondence from set
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Chapter 5 Solutions
A Transition to Advanced Mathematics
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