in a context-free grammara)∈ can’t be the right hand side of any production.b)Terminal symbols can’t be present in the left hand side of any production.c)The number of grammar symbols in the left hand side is not greater than that of in the right hand side.d)All of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

in a context-free grammara)&isin; can&rsquo;t be the right hand side of any production.b)Terminal symbols can&rsquo;t be present in the left hand side of any production.c)The number of grammar symbols in the left hand side is not greater than that of in the right hand side.d)All of the aboveCorrect answer is option 'B'. Can you explain this answer?

Answer

A context-free grammar is a formal grammar that consists of a set of production rules, where each rule defines how to rewrite a nonterminal symbol into a sequence of terminal and/or nonterminal symbols. The rules are applied in any context and do not depend on the surrounding symbols or context.

Context-free grammars are commonly used to describe the syntax of programming languages, natural languages, and other formal languages. They provide a concise and systematic way to generate valid sentences or expressions in these languages.

For example, consider a simple context-free grammar that describes the syntax of arithmetic expressions:

1. S -> E
2. E -> E + T
3. E -> E - T
4. E -> T
5. T -> T * F
6. T -> T / F
7. T -> F
8. F -> (E)
9. F -> num

In this grammar, S is the start symbol, and the rules define how to rewrite nonterminal symbols (S, E, T, F) into sequences of terminal symbols (num, +, -, *, /, (, )). The rules specify the various ways to combine numbers and arithmetic operators to form valid arithmetic expressions.

For example, using this grammar, the expression '2 + 3 * (4 - 1)' can be generated as follows:

S -> E (by applying rule 1)
E -> E + T (by applying rule 2)
E -> T + T (by applying rule 4)
T -> F + T (by applying rule 7)
F -> num + T (by applying rule 9)
F -> 2 + T (by applying rule 9)
F -> 2 + T * F (by applying rule 5)
F -> 2 + F * F (by applying rule 7)
F -> 2 + (E) * F (by applying rule 8)
F -> 2 + (E) * (E) (by applying rule 4)
F -> 2 + (T) * (E) (by applying rule 7)
F -> 2 + (F) * (E) (by applying rule 8)
F -> 2 + (4) * (E) (by applying rule 9)
F -> 2 + (4) * (T) (by applying rule 7)
F -> 2 + (4) * (F) (by applying rule 8)
F -> 2 + (4) * (1) (by applying rule 9)

This sequence of rule applications generates the desired arithmetic expression.

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