Write a recursive grammar for the language of strings where each string contains an 'e' or an 'E' surrounded by any number of digits on both sides. So the following are examples of strings that are in the language: 12345E123, 1e2345, 1E3, 2e4, 22e77 The following are examples of strings that are NOT in the language: E1, 1E, 2e, E, e, 1234E 2. 2. Convert the following infix expression into a postfix expression: (c /( (a + b) * d)). Show your work if you want partial credit - otherwise it will be all or nothing. Place your answer in the space below. 3. Convert the following prefix expression into an infix expression: */+ef-abc. Show your work if you want partial credit - otherwise it will be all or nothing.

Answers

Answer 1

A recursive grammar for the language of strings with an 'e' or an 'E' surrounded by any number of digits on both sides can be defined as follows:

1. S -> D | S D | D S

2. D -> N | N D | D N

3. N -> 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

4. N -> N N

The grammar starts with a start symbol S and expands recursively. The non-terminal symbol S represents the entire string, while D represents a sequence of digits and N represents a single digit.

In the grammar, rule 1 allows for a single digit (D) or a sequence of digits (D) followed by another string (S) or vice versa. Rule 2 allows for concatenation of digits in any order. Rule 3 defines individual digits from 0 to 9. Rule 4 enables the formation of multi-digit numbers.

To generate a string from this grammar, we start with the start symbol S and apply the production rules recursively until we have a valid string in the language. At each step, we randomly select one of the available production rules that match the current non-terminal symbol.

For example, to generate the string "12345E123" from this grammar, we can follow these steps:

- S (start symbol)

- D S (rule 1)

- N D S (rule 2)

- 1 D S (rule 3)

- 1 2 D S (rule 4)

- 1 2 3 D S (rule 4)

- 1 2 3 4 D S (rule 4)

- 1 2 3 4 5 E S (rule 3)

- 1 2 3 4 5 E D (rule 2)

- 1 2 3 4 5 E 1 D (rule 3)

- 1 2 3 4 5 E 1 2 D (rule 4)

- 1 2 3 4 5 E 1 2 3 (rule 4)

The final string "12345E123" is generated following the rules of the grammar, satisfying the required conditions.

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One specific violation that can result in a third-degree felony charge is the unauthorized practice of real estate. This involves engaging in real estate activities without a valid license or certification. It is important to note that the specific laws and penalties can vary depending on the jurisdiction and circumstances of the violation.

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The probability of selecting a vowel from the phrase is 9/37.

To find the probability of selecting a vowel from the phrase "I like to swim at the Recreation Pavilion," we need to determine the number of vowels and the total number of letters in the phrase.

There are five vowels: A, E, I, O, and U.

In the phrase, there are 9 vowels and 37 total letters (spaces are not included). To find the probability, divide the number of vowels by the total number of letters:

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