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
Want to see more full solutions like this?
Chapter 5 Solutions
A Transition to Advanced Mathematics
- Suppose that in an RSA Public Key Cryptosystem. Encrypt the message "algebra" using the -letter alphabet from Example 4. Use two-digit blocks. Use three-digit blocks. What is the secret key?arrow_forward1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2arrow_forwardSuppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal LittellLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning