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The problem asks how many zero-element subsets can be chosen from a two-element set, using Pascal's triangle to find the answer.

### Solution:

1. **Pascal's Triangle**:
   - The rows in Pascal's triangle are indexed starting from \( n = 0 \).
   - Row 2 of Pascal’s triangle corresponds to \( n = 2 \) and is:  
     \[
     1 \quad 2 \quad 1
     \]
     The elements in this row represent the binomial coefficients \( \binom{2}{k} \), where \( k \) ranges from \( 0 \) to \( 2 \).

2. **Subset of size 0**:
   - The number of subsets of size 0 is given by \( \binom{n}{0} \).
   - For \( n = 2 \), \( \binom{2}{0} = 1 \).  
     This means there is exactly **1 subset of size 0**, which is the empty set \( \{\} \).

### Final Answer:
The number of zero-element subsets of a two-element set is **1**.

Would you like me to explain Pascal's triangle further or clarify any concepts?

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Here are some follow-up questions to expand on this:
1. What are the values of \( \binom{2}{k} \) for \( k = 1 \) and \( k = 2 \)?
2. How do the rows of Pascal’s triangle correspond to subsets of a set?
3. Can you explain why \( \binom{n}{0} \) is always equal to 1 for any \( n \)?
4. How does Pascal's triangle relate to the binomial theorem?
5. How would the solution change if the set had 3 elements instead of 2?

**Tip**: The top row of Pascal's triangle (\( n = 0 \)) always corresponds to the case where the set is empty.

How many zero-element subsets can we choose from a two-element set? (Use row 2 of Pascal's triangle to find the answer.)

Learn how to find the number of zero-element subsets from a two-element set using Pascal's triangle. Understand the concept of subsets, binomial coefficients, and properties of Pascal's triangle in this step-by-step explanation, suitable for middle school students.

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