Answered

Experience the power of community-driven knowledge on IDNLearn.com. Ask anything and receive prompt, well-informed answers from our community of knowledgeable experts.

Given [tex]\(A=\{1,2,3\}\)[/tex], [tex]\(B=\{2,4,6\}\)[/tex], and [tex]\(C=\{1,2,3,4,5,6\}\)[/tex], find [tex]\(A \cap (B \cap C)\)[/tex].

A. [tex]\(\emptyset\)[/tex]

B. [tex]\(\{1,2,3,4,5,6,7,8\}\)[/tex]

C. [tex]\(\{2\}\)[/tex]

Sagot :

GinnyAnsweridn
Step-by-Step Solution:

1. Identify the sets:
- Given the sets:
- [tex]\(A = \{1, 2, 3\}\)[/tex]
- [tex]\(B = \{2, 4, 6\}\)[/tex]
- [tex]\(C = \{1, 2, 3, 4, 5, 6\}\)[/tex]

2. Find the intersection of [tex]\(B\)[/tex] and [tex]\(C\)[/tex]:
- [tex]\(B \cap C\)[/tex] is the set of elements that are common to both [tex]\(B\)[/tex] and [tex]\(C\)[/tex].
- That means we look for the common elements in [tex]\(\{2, 4, 6\}\)[/tex] and [tex]\(\{1, 2, 3, 4, 5, 6\}\)[/tex].
- The common elements are [tex]\(\{2, 4, 6\}\)[/tex].

Thus, [tex]\(B \cap C = \{2, 4, 6\}\)[/tex].

3. Find the intersection of [tex]\(A\)[/tex] and [tex]\(B \cap C\)[/tex]:
- [tex]\(A \cap (B \cap C)\)[/tex] is the set of elements that are common to both [tex]\(A\)[/tex] and [tex]\(B \cap C\)[/tex].
- So, we need to find the common elements in [tex]\(\{1, 2, 3\}\)[/tex] and [tex]\(\{2, 4, 6\}\)[/tex].
- The only common element is [tex]\(\{2\}\)[/tex].

Hence, [tex]\(A \cap (B \cap C) = \{2\}\)[/tex].

4. Conclusion:
- The result of [tex]\(A \cap (B \cap C)\)[/tex] is [tex]\(\{2\}\)[/tex].

Therefore, [tex]\(A \cap (B \cap C) = \{2\} \)[/tex].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.