Construct a regular expression for the set of all strings of 0’s and 1’s such that the tenth symbol
from right is 1.

To construct a regular expression for the set of all strings of 0s and 1s such that the tenth symbol from the right is 1, we need to ensure that any string matches the following conditions:

1. There are exactly 9 characters (0 or 1) after the tenth symbol from the right.
2. The tenth symbol from the right is a '1'.
3. There can be any number of characters (0 or 1) before the tenth symbol from the right.

### Regular Expression Explanation

- **`[01]*`**: Matches any number (including zero) of characters that are either '0' or '1'. This represents the portion of the string before the tenth symbol from the right.
  
- **`1`**: Matches exactly one '1', which represents the tenth symbol from the right.

- **`[01]{9}`**: Matches exactly 9 characters that are either '0' or '1'. This represents the nine symbols following the tenth symbol from the right.

### Combining these parts

To ensure the tenth symbol from the right is '1', we construct the regular expression as follows:

\[
\text{Regular Expression} = [01]*1[01]{9}
\]

This regular expression can be explained as:
- **`[01]*`**: Matches any sequence of 0s and 1s of any length before the 1.
- **`1`**: Matches the required '1' that is the tenth symbol from the right.
- **`[01]{9}`**: Matches any sequence of exactly 9 symbols (0s or 1s) that follow the '1'.

### Final Regular Expression

The complete regular expression that represents the set of all strings of 0s and 1s such that the tenth symbol from the right is '1' is:

\[
\text{Regular Expression} = [01]*1[01]{9}
\]

This ensures that any matching string has a '1' as the tenth symbol from the right, followed by any nine characters (0 or 1).

### Would you like more details or have any questions?

#### Related Questions:
1. How would the regular expression change if the condition was that the fifth symbol from the right must be a '0'?
2. How can you modify the regular expression to match strings where the third symbol from the left is '1'?
3. What changes would be necessary to ensure the last symbol in the string is a '1'?
4. Can you create a regular expression to match strings that contain at least two '1's anywhere?
5. How would you construct a regular expression for strings where the number of '1's is exactly three?

#### Tip:
When constructing regular expressions, always start by identifying fixed positions or patterns and then gradually build around them to include any flexible conditions.

Explore how to construct a regular expression for strings of 0s and 1s where the tenth symbol from the right is '1'. Understand the principles behind regular expressions and their application in pattern matching. Suitable for advanced learners and professionals.

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