From everyday questions to specialized queries, IDNLearn.com has the answers. Explore thousands of verified answers from experts and find the solutions you need, no matter the topic.
Sagot :
To find the result for the given sets, we need to perform a couple of set operations. Let's go through the steps in detail.
Given the sets:
[tex]\[ U = \{28, 29, 30, 31, 32, 33, 34, 35, 36, 37\} \][/tex]
[tex]\[ A = \{31, 32, 33, 34\} \][/tex]
[tex]\[ B = \{28, 30, 32, 34, 36\} \][/tex]
[tex]\[ C = \{29, 31, 32, 36, 37\} \][/tex]
### Step 1: Find [tex]\( A \cup B \)[/tex] (Union of A and B)
The union of two sets [tex]\( A \cup B \)[/tex] contains all the elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
[tex]\[ A = \{31, 32, 33, 34\} \][/tex]
[tex]\[ B = \{28, 30, 32, 34, 36\} \][/tex]
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
This union operation includes all distinct elements from both sets.
### Step 2: Find [tex]\( (A \cup B) \cap C \)[/tex] (Intersection of [tex]\( A \cup B \)[/tex] with C)
The intersection of two sets [tex]\( (A \cup B) \cap C \)[/tex] contains all the elements that are in both [tex]\( A \cup B \)[/tex] and [tex]\( C \)[/tex].
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
[tex]\[ C = \{29, 31, 32, 36, 37\} \][/tex]
Now, identify the elements common to both [tex]\( A \cup B \)[/tex] and [tex]\( C \)[/tex]:
[tex]\[ (A \cup B) \cap C = \{31, 32, 36\} \][/tex]
So, the steps yield the following results:
1. The union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\( \{28, 30, 31, 32, 33, 34, 36\} \)[/tex].
2. The intersection of [tex]\( (A \cup B) \)[/tex] with [tex]\( C \)[/tex] is [tex]\( \{31, 32, 36\} \)[/tex].
Thus, the final sets we found are:
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
[tex]\[ (A \cup B) \cap C = \{31, 32, 36\} \][/tex]
Given the sets:
[tex]\[ U = \{28, 29, 30, 31, 32, 33, 34, 35, 36, 37\} \][/tex]
[tex]\[ A = \{31, 32, 33, 34\} \][/tex]
[tex]\[ B = \{28, 30, 32, 34, 36\} \][/tex]
[tex]\[ C = \{29, 31, 32, 36, 37\} \][/tex]
### Step 1: Find [tex]\( A \cup B \)[/tex] (Union of A and B)
The union of two sets [tex]\( A \cup B \)[/tex] contains all the elements that are in [tex]\( A \)[/tex], in [tex]\( B \)[/tex], or in both.
[tex]\[ A = \{31, 32, 33, 34\} \][/tex]
[tex]\[ B = \{28, 30, 32, 34, 36\} \][/tex]
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
This union operation includes all distinct elements from both sets.
### Step 2: Find [tex]\( (A \cup B) \cap C \)[/tex] (Intersection of [tex]\( A \cup B \)[/tex] with C)
The intersection of two sets [tex]\( (A \cup B) \cap C \)[/tex] contains all the elements that are in both [tex]\( A \cup B \)[/tex] and [tex]\( C \)[/tex].
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
[tex]\[ C = \{29, 31, 32, 36, 37\} \][/tex]
Now, identify the elements common to both [tex]\( A \cup B \)[/tex] and [tex]\( C \)[/tex]:
[tex]\[ (A \cup B) \cap C = \{31, 32, 36\} \][/tex]
So, the steps yield the following results:
1. The union of sets [tex]\( A \)[/tex] and [tex]\( B \)[/tex] is [tex]\( \{28, 30, 31, 32, 33, 34, 36\} \)[/tex].
2. The intersection of [tex]\( (A \cup B) \)[/tex] with [tex]\( C \)[/tex] is [tex]\( \{31, 32, 36\} \)[/tex].
Thus, the final sets we found are:
[tex]\[ A \cup B = \{28, 30, 31, 32, 33, 34, 36\} \][/tex]
[tex]\[ (A \cup B) \cap C = \{31, 32, 36\} \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Discover the answers you need at IDNLearn.com. Thanks for visiting, and come back soon for more valuable insights.