https://file.aiquickdraw.com/mathbot/file/1726016489890p6nbwxur.jpg

Let's go through the Venn diagram problem.

The universal set \( U \) contains the subjects:
- Art
- Bio (Biology)
- Chem (Chemistry)
- Econ (Economics)
- English
- German
- Math
- Psych (Psychology)
- Stats

### (a) Set: \( M \cap F \)
This is the intersection of the sets \( M \) and \( F \), meaning the subjects that are offered on both Monday and Friday.

From the Venn diagram, the subjects common to both \( M \) and \( F \) are:
- Bio (Biology)
- Econ (Economics)

**Roster form**: \( M \cap F = \{ \text{Bio, Econ} \} \)

### (b) Set: \( (F \cup M)' \)
This is the complement of the union of sets \( M \) and \( F \). The union \( F \cup M \) represents all the subjects offered either on Monday, Friday, or both. According to the Venn diagram, these subjects are:
- English
- Bio (Biology)
- Econ (Economics)
- Chem (Chemistry)
- German
- Psych (Psychology)

The complement of this set is everything in the universal set \( U \) that is not in \( F \cup M \). From the universal set \( U \), the subjects not included in \( F \cup M \) are:
- Art
- Stats
- Math

**Roster form**: \( (F \cup M)' = \{ \text{Art, Stats, Math} \} \)

Let me know if you need further details or clarification!

### Related questions:
1. What is the union of the sets \( M \) and \( F \)?
2. What is the complement of set \( F \)?
3. How can we interpret the difference between \( M \) and \( F \)?
4. How would you represent \( M \cup F \) in descriptive form?
5. What would be the result of the complement of \( M \cap F \)?

**Tip**: Always visualize Venn diagrams as a way to understand set operations better.

Use the Venn diagram to write the descriptive and roster forms of the sets below: (a) M ∩ F, (b) (F ∪ M)'

Solve the Venn diagram problem by finding the intersection of sets M and F, as well as the complement of the union of M and F. This problem explores key set theory concepts such as intersection, union, and complement, perfect for students in Grades 6-9.

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