We consider the set E={1;2;3;4;5}
. A is the subset of E constituted by even integers. B is the subset of E constituted by odd integers. C is the subset of E constituted by the powers of 2. What elements does D=(A∩C)∪B
contain ?

Select one:

D=E

D={2;4}

D={1;3;5}

None of the proposed choices

D=∅

To solve for the set \( D = (A \cap C) \cup B \), we first need to define the sets \( A \), \( B \), and \( C \) based on the set \( E = \{1, 2, 3, 4, 5\} \):

1. **Set \( A \)** (even integers in \( E \)):
   \[
   A = \{2, 4\}
   \]

2. **Set \( B \)** (odd integers in \( E \)):
   \[
   B = \{1, 3, 5\}
   \]

3. **Set \( C \)** (powers of 2 in \( E \)):
   The powers of 2 in the set \( E \) are:
   \[
   C = \{1, 2, 4\}
   \]

Next, we calculate the intersection \( A \cap C \):
\[
A \cap C = \{2, 4\} \cap \{1, 2, 4\} = \{2, 4\}
\]

Now, we calculate \( D \):
\[
D = (A \cap C) \cup B = \{2, 4\} \cup \{1, 3, 5\} = \{1, 2, 3, 4, 5\}
\]

Thus, \( D = E \).

**Answer: \( D = E \)**.

If you have any questions or need further details, feel free to ask! Here are some related questions:

1. What are the properties of set operations such as union and intersection?
2. How can we identify all the subsets of a given set?
3. What is the significance of powers of integers in set theory?
4. How would the result change if \( E \) included negative integers?
5. Can you provide examples of other set operations with different sets? 

**Tip:** When working with sets, always list the elements clearly to avoid confusion, especially when performing operations like union or intersection.

We consider the set E={1;2;3;4;5}. A is the subset of E constituted by even integers. B is the subset of E constituted by odd integers. C is the subset of E constituted by the powers of 2. What elements does D=(A∩C)∪B contain?

Explore the union and intersection of subsets in set theory with the problem involving the sets E, A, B, and C. Learn how to determine the elements of D and understand the key concepts of even integers, odd integers, and powers of 2.

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