1. Give the leftmost and rightmost derivations corresponding to each of the derivation trees given in Figure 3.3.
2. For each of the following context-free grammars, use set notation to define the language generated by the grammar.
The Correct Answer and Explanation is :
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1. Leftmost and Rightmost Derivations
A leftmost derivation means you always replace the leftmost non-terminal first, and a rightmost derivation means you always replace the rightmost non-terminal. To find the derivations, examine the derivation tree and list out how the start symbol evolves by applying the production rules in each case.
2. Context-Free Grammars (CFGs) and Set Notation
To define the language of a CFG in set notation, you:
- Identify the start symbol of the grammar.
- List the production rules and deduce the structure of strings they generate.
- Use set notation, for example:
{ w | w is a string derived from the start symbol S using the production rules }.
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