Use the given sets to find |D∪E||D∪E|.

U={a,b,c,d,…,x,y,z}U={a,b,c,d,…,x,y,z}

D={q,u,o,t,e}D={q,u,o,t,e}

E={b,a,r,o,q,u,e}E={b,a,r,o,q,u,e}

To find \( |D \cup E| \), the cardinality (size) of the union of sets \( D \) and \( E \), we first need to determine the elements in \( D \cup E \), which represents all unique elements from both sets \( D \) and \( E \).

Given:
- \( D = \{ q, u, o, t, e \} \)
- \( E = \{ b, a, r, o, q, u, e \} \)

### Step 1: Find the Union of \( D \) and \( E \)
The union \( D \cup E \) includes all elements that are in either set \( D \) or \( E \) (or both), without repeating any elements.

- Elements in \( D \): \( \{ q, u, o, t, e \} \)
- Elements in \( E \): \( \{ b, a, r, o, q, u, e \} \)

Now combine these two sets, eliminating duplicates:
\[
D \cup E = \{ q, u, o, t, e, b, a, r \}
\]

### Step 2: Find the Cardinality of \( D \cup E \)
Now, count the unique elements in \( D \cup E \):
\[
|D \cup E| = 8
\]

Thus, the cardinality of \( D \cup E \) is \( \boxed{8} \).

Would you like any further explanation or details on this?

Here are 5 related questions for further practice:
1. What is \( |D \cap E| \), the cardinality of the intersection of \( D \) and \( E \)?
2. Find \( |E^c| \), the complement of set \( E \) relative to \( U \).
3. How many elements are in \( D^c \cup E \), where \( D^c \) is the complement of set \( D \)?
4. If \( F = \{ p, s, o, l, i, d \} \), what is \( |D \cup F| \)?
5. Find the symmetric difference \( D \Delta E \), which is the set of elements in either \( D \) or \( E \), but not in both.

**Tip:** When combining sets, always ensure to remove duplicates to accurately determine the union.

Use the given sets to find |D∪E|. U={a,b,c,d,…,x,y,z} D={q,u,o,t,e} E={b,a,r,o,q,u,e}

Discover how to calculate the cardinality of the union of sets D={q,u,o,t,e} and E={b,a,r,o,q,u,e} with a step-by-step solution. This problem explores key set theory concepts like union and cardinality, ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation