The document you uploaded contains a review sheet for a mathematics course (MATH 119, Fall 2024). It includes various problems from set theory, combinatorics, number theory, logic, and statistics. Below is an overview of the key problems mentioned:

1. Set Theory and Venn Diagrams: Subsets, intersections, and unions involving sets of animals, mammals, fish, and specific animals.
2. Permutations: Calculating arrangements of letters in a word ("TERRIBLE").
3. Combination Choices: Movie-watching combinations and t-shirt purchase possibilities.
4. Data and Statistics: Constructing sets with the same mean but different medians; calculating descriptive statistics and creating a box-and-whisker plot.
5. Fractions and Arithmetic: Operations with fractions and integers.
6. Least Common Multiple (LCM): Situations where the LCM isn't the product of two numbers.
7. Logic: Transforming and analyzing statements, their converse, and contrapositive.
8. Allocation Problems: Comparing profit shares and satisfying fractional pizza requests.
9. Contest Prizes: Ranking combinations for a contest.
10. Divisibility and Number Theory: GCF and LCM properties based on divisibility.

Would you like detailed solutions to any of these problems?

Follow-up Questions:

1. Do you need clarification on how to draw the Venn diagram for Problem 1?
2. Should I calculate the total arrangements for "TERRIBLE" in Problem 2?
3. Would you like help with interpreting fractional allocations in Problem 11?
4. Should I solve the statistics problem (mean, median, mode, etc.) in Problem 14?
5. Do you want to discuss logical equivalences in Problem 9?

Tip:

For any set-based problem, start by clearly defining the relationships among the sets (e.g., subsets, disjoint, or overlapping) to simplify the operations.