In a ounce bag of Skittles, Jeri found red Skittles, purple Skittles, and yellow Skittles. Jeri made the

following conjecture:“Each Skittles bag has at least of each Skittle color." Decide if each statement would

prove, disprove, or neither prove nor disprove her conjecture.

2.17 5 12 14

5

In a new 2.17 ounce bag of Skittles, no purple Skittles were found.

There were a total of 100 red Skittles found in ten 2.17 ounce bags of candy.

No 2.17 ounce bags of Skittles contain the same number of each Skittle color.

Let's analyze each statement to determine whether it would **prove**, **disprove**, or **neither prove nor disprove** Jeri's conjecture that "Each Skittles bag has at least one of each Skittle color."

### Conjecture: "Each Skittles bag has at least one of each Skittle color."

#### 1. **"In a new 2.17-ounce bag of Skittles, no purple Skittles were found."**

- **Analysis**: This directly contradicts the conjecture because it shows a situation where a Skittles bag does **not** have at least one of each color.
- **Conclusion**: This statement **disproves** the conjecture.

#### 2. **"There were a total of 100 red Skittles found in ten 2.17-ounce bags of candy."**

- **Analysis**: This statement only provides information about the red Skittles across multiple bags. It does not address whether each bag contains at least one of each color.
- **Conclusion**: This statement **neither proves nor disproves** the conjecture.

#### 3. **"No 2.17-ounce bags of Skittles contain the same number of each Skittle color."**

- **Analysis**: This statement suggests variation in the number of each color across bags but does not indicate whether there is at least one of each color in every bag. The conjecture is about the presence of each color, not the quantity.
- **Conclusion**: This statement **neither proves nor disproves** the conjecture.

### Summary:
- The first statement disproves the conjecture.
- The second and third statements neither prove nor disprove the conjecture.

Would you like more details on any part of this reasoning? Here are 5 related questions you might consider:

1. What is the difference between proving and disproving a conjecture?
2. Can you explain more about how counterexamples work in logic?
3. How could you design an experiment to test Jeri's conjecture more thoroughly?
4. What are some common pitfalls in making logical conjectures?
5. Can you explain how to strengthen or modify a conjecture when it has been disproved?

**Tip:** When evaluating a conjecture, always look for counterexamples, as they can quickly disprove the statement.

Explore how statements in logic and set theory can disprove conjectures. Analyze Jeri's conjecture about Skittles bags and learn when statements prove, disprove, or neither prove nor disprove a conjecture. Suitable for Grades 7-9.

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