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Chapter 2: Problem 100

Find the cardinal sum \(4+5\) of the two finite cardinal numbers 4 and 5 .

Short Answer

Expert verified
The cardinal sum of the numbers 4 and 5 is 9.

Step by step solution

01

Identify the Given Numbers

We are given the finite cardinal numbers, 4 and 5 and are asked to find their sum. In mathematical notation, this is written as: \(4 + 5\)
02

Add the Numbers

Now, we will add the numbers. Using basic arithmetic, we find the sum as follows: \[4 + 5 = 9\]
03

Write the Final Answer

The cardinal sum of the numbers 4 and 5 is 9.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Finite Set
In mathematics, a finite set is a collection of distinct items that have a specific, countable number of elements. Consider a set that includes items you can count on your fingers, like the numbers 1 through 5. A finite set has an end, meaning you can eventually count all the items and reach a final number.

Finite sets are everywhere in real life and math. If we think of the numbers in our exercise, 4 and 5, they each represent distinct finite sets. The number 4 represents a set of four items, while 5 represents a set of five items. Together, these numbers are involved in operations like addition, giving us insights into basic numerical concepts like cardinality.
  • A finite set can be described by listing its elements or stating its size.
  • The actual content isn鈥檛 as crucial for arithmetic operations; what matters is the number of elements.
  • Finite sets are comfortable for beginners because they are manageable and easy to understand.
Basic Arithmetic
Basic arithmetic involves operations such as addition, subtraction, multiplication, and division. These are the building blocks of all math, providing simple rules to manipulate numbers. Addition, like in the exercise, takes two numbers and combines them into a new sum.

Think of basic arithmetic as the way we count and calculate everyday things: totaling prices, counting objects, or measuring ingredients. In the expression \(4 + 5\), we're using basic arithmetic to combine these finite cardinal numbers to find their total.
  • Addition is often the first and most intuitive arithmetic operation learned.
  • Understanding basic arithmetic is essential for more advanced mathematical concepts.
  • This process doesn鈥檛 change, regardless of what numbers you are working with.
Cardinal Sum
The concept of a cardinal sum refers to the result of combining the sizes of two sets. When we talk about the cardinal sum of 4 and 5, we are asking, "How many elements are there in total?"

For finite sets, the cardinal sum is simply the arithmetic sum. In our example, adding cardinal numbers 4 and 5 gives 9. This sum represents the total count of elements if you merged two distinct groups, one with four items and another with five.
  • Cardinal sums help us grasp the concept of counting combined elements in sets.
  • They are a foundational idea in understanding larger mathematical operations.
  • The result of a cardinal sum is always a single number representing the combined count.
By understanding cardinal sums, we prepare ourselves for more complex mathematical concepts, laying the groundwork for learning about infinite sets and their properties.

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Most popular questions from this chapter

Given \(\mathrm{A}=\\{2,4,6\\}\) and \(\mathrm{B}=\\{\mathrm{y} \mid 1 \leq \mathrm{y} \leq 4\) and \(\mathrm{y} \in \mathrm{R}\\}\), sketch the graph of \(\mathrm{A} \times \mathrm{B}\).

Prove that the power set \(\mathrm{P}(\mathrm{A})\) of any set \(\mathrm{A}\) of \(\mathrm{n}\) elements contains exactly \(2^{\mathrm{n}}\) elements.

State the law of set operations.

A survey of 100 people was conducted to determine the popularity of three local radio stations; V.P.H.K, B.A.P.C and W.P.Q.W. The results were as follows: 42 people liked VPHK 48 people liked BAPC 41 people liked WPQW 15 people liked both VPHK and BAPC 17 people liked both VPHK and WPQW 18 people liked both BAPC and WPQW 10 people liked all the three radio Find the number of people who liked none of the three stations.

In a freshman class of 200 students of a certain college, records indicate that 80 students registered to take Biology \(\mathrm{I}\), 90 registered to take Calculus I, 55 registered to take General Physics I, 32 registered to take both Biology I and Calculus I, 23 registered to take both Calculus I and General Physics I, 16 registered to take both Biology I and General Physics \(\mathrm{I}\), and 8 registered to take all three courses. Is the record from the registrar's office accurate? (Assume that each of the 200 students registered for at least one course.)
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