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Let A = {H, T}, B = {1, 2, 3, 4, 5, 6}, and C = {red}. Find the number indicated. n(A x C x C)

Let A = {H, T}, B = {1, 2, 3, 4, 5, 6}, and C = {red}. Find the number indicated. n(A x C x C)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let A = {H, T}, B = {1, 2, 3, 4, 5, 6}, and C = {red}. Find the number indicated.
n(A ✕ C ✕ C)
 
**Educational Content: Understanding Cartesian Products** Given sets: - \( A = \{ H, T \} \) - \( B = \{ 1, 2, 3, 4, 5, 6 \} \) - \( C = \{ \text{red} \} \) **Objective:** Find the number of elements in the Cartesian product \( A \times C \times C \). **Explanation:** - A Cartesian product of sets is an ordered pair of sets that provides all possible combinations of elements. - \( A \times C \times C \) means we are creating ordered triples where the first element is from set \( A \), the second and third elements are from set \( C \). **Steps:** 1. Since \( A \) has 2 elements, and \( C \) has 1 element, \( C \times C \) will have \( 1 \times 1 = 1 \) element. 2. Therefore, \( A \times C \times C \) = \( 2 \times 1 = 2 \) combinations. **Conclusion:** The number of elements in \( A \times C \times C \) is **2**. **Note:** No graphs or diagrams are included with this problem.
Transcribed Image Text:**Educational Content: Understanding Cartesian Products** Given sets: - \( A = \{ H, T \} \) - \( B = \{ 1, 2, 3, 4, 5, 6 \} \) - \( C = \{ \text{red} \} \) **Objective:** Find the number of elements in the Cartesian product \( A \times C \times C \). **Explanation:** - A Cartesian product of sets is an ordered pair of sets that provides all possible combinations of elements. - \( A \times C \times C \) means we are creating ordered triples where the first element is from set \( A \), the second and third elements are from set \( C \). **Steps:** 1. Since \( A \) has 2 elements, and \( C \) has 1 element, \( C \times C \) will have \( 1 \times 1 = 1 \) element. 2. Therefore, \( A \times C \times C \) = \( 2 \times 1 = 2 \) combinations. **Conclusion:** The number of elements in \( A \times C \times C \) is **2**. **Note:** No graphs or diagrams are included with this problem.
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