Let's analyze and solve the problem.

Given Data:

• Universal Set $U = \{a, b, c, d, e, f, g, h, i, j\}$
• Set $V$ = {a, e, i, f, h}
• Set $W$ = {a, c, e, g, i}

We are asked to list the members of $\overline{V} \cup \overline{W}$, where:

• $\overline{V}$ is the complement of $V$, meaning all elements in $U$ that are not in $V$.
• $\overline{W}$ is the complement of $W$, meaning all elements in $U$ that are not in $W$.
• The union $\overline{V} \cup \overline{W}$ represents all elements that are in either $\overline{V}$ or $\overline{W}$.

Step 1: Find $\overline{V}$ and $\overline{W}$

1. Complement of $V$:

   • Elements in $U$ but not in $V$: $\overline{V} = \{b, c, d, g, j\}$

2. Complement of $W$:

   • Elements in $U$ but not in $W$: $\overline{W} = \{b, d, f, h, j\}$

Step 2: Find $\overline{V} \cup \overline{W}$

To find the union of $\overline{V}$ and $\overline{W}$, combine all unique elements from both sets:

$\overline{V} \cup \overline{W} = \{b, c, d, g, j, f, h\}$

Solution

The members of $\overline{V} \cup \overline{W}$ are: $\{b, c, d, f, g, h, j\}$

Would you like more details on any step, or have any questions?

Related Questions:

1. How would the answer change if $U$ had additional elements?
2. What is the result of $V \cap W$, and how does it relate to the complements?
3. How would $\overline{V} \cap \overline{W}$ differ from $\overline{V} \cup \overline{W}$?
4. If $V$ or $W$ was empty, what would $\overline{V} \cup \overline{W}$ be?
5. How can we represent $\overline{V} \cup \overline{W}$ using a Venn diagram?

Tip:

Always remember that the complement of a set contains all elements not in the set, but within the universal set $U$.