The task involves set theory. Let me clarify the problem and break it down step by step.

We are given:

• Universal set $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$
• Sets:
  • $A = \{1, 2, 3, 4, 5, 9\}$
  • $B = \{2, 4, 6, 8\}$
  • $C = \{1, 3, 5, 7\}$
  • $D = \{1, 2, 4, 5, 7, 8, 9\}$
• Set $F = \{2, 4, 6, 8, 9\}$

We are asked to express $F$ in terms of sets $U, A, B, C, D$.

Step 1: Analyze Set $F$

Set $F$ is $\{2, 4, 6, 8, 9\}$.

Step 2: Compare $F$ with Other Sets

1. Check intersections:

   • $B = \{2, 4, 6, 8\}$, so $B \subset F$ (all elements of $B$ are in $F$).
   • $A = \{1, 2, 3, 4, 5, 9\}$: elements $2, 4, 9 \in A$ are also in $F$.
   • $D = \{1, 2, 4, 5, 7, 8, 9\}$: elements $2, 4, 8, 9 \in D$ are also in $F$.

2. Uniqueness:

   • The only element in $F$ that is not part of $A$ or $C$ is $6$, which appears only in $B$.

Step 3: Represent $F$

From the analysis above:

• $F$ can be written as the union of $B$ (contains $2, 4, 6, 8$) and the element $9$ (from $A$ or $D$).

Thus: $F = B \cup \{9\}.$

Final Answer:

The set $F$ can be expressed as: $F = B \cup \{9\}.$

Let me know if you need further clarification or additional details!

Related Questions:

1. What is the complement of set $B$ relative to $U$?
2. How can set $C \cap D$ be represented?
3. Find the difference $A - B$.
4. What is the intersection $A \cap D$?
5. Is $F \subset U$? Explain.

Tip:

When working with sets, always compare elements systematically to determine unions, intersections, or complements. This makes expressions more precise!