A = {13,22,31,40} and B= {14,22,41} then value *n*(*A*∪*B*)= ?

Given the sets \( A \) and \( B \):

\[ A = \{13, 22, 31, 40\} \]
\[ B = \{14, 22, 41\} \]

We need to find the number of elements in the union of sets \( A \) and \( B \), denoted as \( A \cup B \).

### Union of Sets \( A \) and \( B \)
The union of two sets contains all unique elements from both sets. Let's list all the elements from \( A \) and \( B \):

- From \( A \): \( 13, 22, 31, 40 \)
- From \( B \): \( 14, 22, 41 \)

Now, combine these lists and remove any duplicates:

\[ A \cup B = \{13, 22, 31, 40, 14, 41\} \]

### Counting the Elements
Count the number of unique elements in \( A \cup B \):

- \( 13 \)
- \( 22 \)
- \( 31 \)
- \( 40 \)
- \( 14 \)
- \( 41 \)

There are 6 unique elements.

Thus, the value of \( n(A \cup B) \) is:

\[ n(A \cup B) = 6 \]

Would you like details or have any questions about this problem? Here are some related questions for further practice:

1. Find \( n(A \cap B) \) for the sets defined above.
2. Determine \( n(A \setminus B) \).
3. Determine \( n(B \setminus A) \).
4. If \( C = \{ x : x \text{ is a two-digit number such that the difference of its digits is 4} \), find \( n(A \cup C) \).
5. If \( D = \{ x : x \text{ is a two-digit number such that the sum of its digits is 6} \), find \( n(D \cup B) \).
6. Verify if any element in \( A \cap B \) exists.
7. Find the total number of two-digit numbers where the sum of the digits is 5.
8. Find the total number of two-digit numbers where the product of the digits is 6.

**Tip:** When dealing with sets and their unions and intersections, it's helpful to list out the elements clearly to avoid double-counting.

Learn how to calculate the number of elements in the union of sets A and B. Given sets A = {13, 22, 31, 40} and B = {14, 22, 41}, find n(A ∪ B). This problem covers basic set theory, union of sets, and counting unique elements. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation