Consider the following grammar:
E  T E’
E’  +T E’ | ɛ
T  F T’
T’  *F T’ | ɛ
F (E) | id
i. Calculate first() and follow() from above grammar.
ii. Draw LL(1) Parsing table from the following grammar.
iii. Check Validity of the string “id * id + id

To address the given problem, we'll tackle it in three parts:

### 1. **Calculate First() and Follow() Sets**

Let's go step by step through the grammar.

#### Grammar Rules:
1. \( E \to T \ E' \)
2. \( E' \to + \ T \ E' \ | \ \varepsilon \)
3. \( T \to F \ T' \)
4. \( T' \to * \ F \ T' \ | \ \varepsilon \)
5. \( F \to ( \ E \ ) \ | \ id \)

#### **First Sets**

**First(E):**
- \( E \to T \ E' \)
- First(E) = First(T)

**First(T):**
- \( T \to F \ T' \)
- First(T) = First(F)

**First(F):**
- \( F \to ( \ E \ ) \) or \( F \to id \)
- First(F) = { '(', 'id' }

So, \( \text{First}(T) = \text{First}(F) = \{ '(', 'id' \} \)
Thus, \( \text{First}(E) = \{ '(', 'id' \} \)

**First(E'):**
- \( E' \to + \ T \ E' \ | \ \varepsilon \)
- First(E') = { '+', \( \varepsilon \) }

**First(T'):**
- \( T' \to * \ F \ T' \ | \ \varepsilon \)
- First(T') = { '*', \( \varepsilon \) }

**Summary of First Sets:**
- \( \text{First}(E) = \{ '(', 'id' \} \)
- \( \text{First}(E') = \{ '+', \varepsilon \} \)
- \( \text{First}(T) = \{ '(', 'id' \} \)
- \( \text{First}(T') = \{ '*', \varepsilon \} \)
- \( \text{First}(F) = \{ '(', 'id' \} \)

#### **Follow Sets**

**Follow(E):**
- \( E \to T \ E' \), \( F \to ( \ E \ ) \)
- \( \) appears in Follow(E) since \( E \) appears in the rule \( F \to ( \ E \ ) \).
- Follow(E) includes all symbols from Follow(F).

**Follow(E’):**
- \( E' \to +T \ E' \)
- Since \( E' \) follows T **

Explore how to calculate First() and Follow() sets for a given context-free grammar. This problem involves analyzing the grammar rules and determining the sets necessary for parsing algorithms. Suitable for advanced university-level students and researchers in formal languages and automata theory.

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