Question

For the grammar \[ E\rightarrow E*F\;|\;F+E\;|\;F \] \[ F\rightarrow F-F\;|\;id \] Which statement is true?

• A. * has higher precedence than +
• B. - has higher precedence than *
• C. + and - have same precedence
• D. + has higher precedence than *

Hint:

Lower grammar levels imply higher operator precedence.

Answer 1

The Correct Option is B

Concept: Operators appearing lower in the grammar hierarchy have higher precedence.

Step 1: Observe non-terminal levels.
\[ E\rightarrow E*F \] uses \(F\). \[ F\rightarrow F-F \] contains operator \(-\).

Step 2: Determine precedence.
Since \(-\) appears inside \(F\), it binds more strongly than operators defined at level \(E\). Thus \[ -\;>\;* \] in precedence.

Step 3: Write answer.
Therefore option (B) is correct.