show a parse tree and a leftmost derivation for each of the following statements: 1. \( A = A \times (B + (C \times A)) \)2. \( B = C \times (A \times C + B) \)3. \( A = A \times (B + C) \)

Answered: 1. A = A * (B + (C * A)) 2. BC* (A* C +…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

show a parse tree and a leftmost derivation for each of the following statements:

1. \( A = A \times (B + (C \times A)) \)

2. \( B = C \times (A \times C + B) \)

3. \( A = A \times (B + C) \)

Expert Solution

Step 1: Explanation

SOLUTION -

A parse tree, also known as a syntax tree, is a graphical representation of the syntactic structure of a sentence or a statement according to a formal grammar.

(1) A = A * (B + (C * A))

Parse Tree:

leftmost derivation:

assign> => <id> = <expr>
=> A = <expr>
=> A = <id> * <expr>
=> A = A * <expr>
=> A = A * ( <expr> )
=> A = A * ( <id> + <expr> )
=> A = A * ( B + <expr> )
=> A = A * (B + ( <expr> ))
=> A = A * (B + ( <id> * <expr> ))
=> A = A * (B + ( C * <expr> ))
=> A = A * (B + ( C * <id> ))
=> A = A * (B + ( C * A ))

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