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The assignment you provided includes a variety of questions involving Venn diagrams, set relations, functions, and evaluating equations. Here's a breakdown of the problems:

1. **Venn Diagram Problem 1 (Students and Games):**
   - 140 students surveyed.
   - 60 like video games, 70 like indoor games, 75 like outdoor games.
   - 30 play indoor and outdoor games.
   - 18 play video games and outdoor games.
   - 42 play video games and indoor games.
   - 8 play all types of games.
   - Questions:
     1. How many students play only outdoor games?
     2. How many students play video games and indoor games, but not outdoor games?

2. **Venn Diagram Problem 2 (Women and Movie Genres):**
   - Survey of 1000 women.
   - 52% like comedies, 45% like fantasy, 60% like romantic movies.
   - 25% like both comedy and fantasy.
   - 28% like both romantic and fantasy.
   - 30% like both comedy and romantic.
   - 6% like none of the genres.
   - Questions:
     1. How many women like all three genres?
     2. How many women like only one of the three genres?
     3. How many women like at least two of the given genres?

3. **Mapping Diagram and Graph:**
   - Two sets of points:
     1. \{(-2, 3), (4, 5), (6, -5), (-2, 3)\}
     2. \{(-2, 1), (4, 3), (7, -3)\}
   - Determine if they represent a relation and function.

4. **Equation Evaluation:**
   - Equation: \( x = 4y^2 - 2y \)
   - Complete the table by evaluating the equation for the given values of \( y \).

Would you like me to walk you through the solution process for each of these problems?

Here are five follow-up questions that could expand your understanding of these problems:
1. How is the formula for intersection and union of sets used in solving Venn diagram problems?
2. How do you determine if a relation is a function based on a mapping diagram?
3. What is the best approach to evaluate an equation for multiple values of a variable?
4. How can you use percentages to find actual numbers in survey results?
5. What are the steps to correctly draw a Venn diagram with three sets?

**Tip**: When working with Venn diagrams, it helps to start by filling in the information from the innermost region (those belonging to all sets) and work your way outward to ensure no overlaps are missed.

Using the Venn diagram solve the following problems:
1. In a survey among 140 students, 60 like video games, 70 like indoor games, 75 like outdoor games, 30 play indoor and outdoor games, 18 like video games and outdoor games, 42 like video games and indoor games, and 8 like all types of games. Find:
  a. How many students play only outdoor games?
  b. How many students play video games and indoor games but not outdoor games?

2. In a survey of 1000 women, 52% liked comedies, 45% liked fantasy, 60% liked romantic movies, 25% liked both comedy and fantasy, 28% liked both romantic and fantasy, and 30% liked both comedy and romantic. 6% liked none of these genres. Find:
  a. How many women like all three genres?
  b. How many women like only one genre?
  c. How many women like at least two genres?

3. Illustrate the following sets in a Mapping Diagram and identify if they represent a relation and function:
  - {(-2, 3), (4, 5), (6, -5), (-2, 3)}
  - {(-2, 1), (4, 3), (7, -3)}

4. Complete the table by evaluating the equation x = 4y^2 – 2y.

This exercise covers solving Venn diagram problems involving set operations, analyzing mapping diagrams for functions, and evaluating quadratic-like equations. Learn how to approach survey-based problems and identify functions in high school-level math.

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