Consider the grammar defined by the following production rules, with two operators * and + S T * P T U T * U P Q + P Q Q Id U Id Which one of the following is TRUE? A) + is left associative, while * is right associative B) + is right associative, while * is left associative C) Both + and * are right associative D) Both + and * are left associative

Official answer: B) + is right associative, while * is left associative. Explanation: To determine the associativity of operators from context-free grammar productions: 1. **For operator $*:** The production rule is T T * U U. Since the non-terminal T appears on the leftmost position on the right-hand side (T T * U), the production is left-recursive. Therefore, the operator * is left-associative. 2. For operator $+: The production rule is P Q + P Q. Since the non-terminal P appears on the rightmost position on the right-hand side (P Q + P), the production is right-recursive. Therefore, the operator + is right-associative. Hence, + is right associative, while * is left associative, which corresponds to option (B).

A) + is left associative, while * is right associative

B) + is right associative, while * is left associative

C) Both + and * are right associative

D) Both + and * are left associative

Compiler Design · Parsing

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

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GATE CSE 2014 Set 2 Q17 · MCQ · 1 mark

Consider the grammar defined by the following production rules, with two operators $$ and $+$ $S \rightarrow T P$ $T \rightarrow U \mid T * U$ $P \rightarrow Q + P \mid Q$ $Q \rightarrow Id$ $U \rightarrow Id$ Which one of the following is TRUE?

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Parsing

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How GATE tests Parsing

GATE heavily tests the Parsing stage of compiler design across both Top-Down (LL(1), recursive descent) and Bottom-Up (LR(0), SLR(1), LALR(1), CLR(1)) paradigms. Key evaluation areas include computing FIRST and FOLLOW sets to populate parsing tables, detecting conflicts (Shift-Reduce, Reduce-Reduce), classifying grammars within the parsing power hierarchy, and executing item-set closure/goto operations. In recent years, items have shifted toward exact item counting via GOTO/CLOSURE in NAT format, reverse engineering grammar rules from FIRST/FOLLOW sets, and multi-concept MSQ verification.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Compiler Design · Parsing

Official IIT answer key · IIT Kharagpur · Audited Aug 2026

Take topic test

GATE CSE 2014 Set 2 Q17 · MCQ · 1 mark

Consider the grammar defined by the following production rules, with two operators $$ and $+$ $S \rightarrow T P$ $T \rightarrow U \mid T * U$ $P \rightarrow Q + P \mid Q$ $Q \rightarrow Id$ $U \rightarrow Id$ Which one of the following is TRUE?

Select an option to check

Key concept

Parsing

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Parsing

Full Parsing guide →

More on Parsing

All 23 questions on Parsing →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Consider the grammar defined by the following production rules, with two operators $$ and $+$ $S \rightarrow T P$ $T \rightarrow U \mid T * U$ $P \rightarrow Q + P \mid Q$ $Q \rightarrow Id$ $U \rightarrow Id$ Which one of the following is TRUE?

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Consider the grammar defined by the following production rules, with two operators $$ and $+$ $S \rightarrow T P$ $T \rightarrow U \mid T * U$ $P \rightarrow Q + P \mid Q$ $Q \rightarrow Id$ $U \rightarrow Id$ Which one of the following is TRUE?

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