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I have an exam just the day after tomorrow. Please help me with this question and explain me the answer so that i could do all questions of this level in my exam.

Grammar is

E-> E/X | X
X-> T-X | X*T | T
T-> T+F | F
F-> (E) | id

id stands for identifier.

Q1 : Above grammar is used to generate all valid arithmetic expressions in a hypothetical language in which 

a. / associates from the left
b. * associative from the left
c. + associative from the left
d. all of these

Q 2 : Above grammar is used to generate all valid arithmetic expressions in a hypothetical language in which

a.  + has the highest precedence
b.  * has the highest precedence
c.  - has the highest precedence
d.  / has the highest precedence
Meghan
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    This question appears to be off-topic because it is about a theoretical quastion, not an implementation problem. Might be better for Programmers.SE – Seki Feb 28 '14 at 10:23
  • A good question indeed. Read this answer [Unambiguous grammar for exponentiation operation](http://stackoverflow.com/a/17170820/1673391) comment me back if you have doubts in my answer. – Grijesh Chauhan Feb 28 '14 at 14:46
  • Possible duplicate of [Unambiguous grammar for exponentiation operation](http://stackoverflow.com/questions/17162919/unambiguous-grammar-for-exponentiation-operation) – Brian Tompsett - 汤莱恩 Aug 23 '16 at 10:25

1 Answers1

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let's put the level at each statements

E-> E/X | X....................1(root)
X-> T-X | X*T | T..............2
T-> T+F | F....................3
F-> (E) | id...................4

Precedence

op which is in the max level has the max precedence so id, (, ) has highest precedence folowed by + then -,* then /

so + has the highest precedence as per option

Associativity

Note A->Ax is left recursive and A-xA is right recursive grammer Now 

E-> E/X  is left recursive so / is left associated
X-> T-X is right recursive so - is right associated
X->  X*T is left recursive so / is left associated
T-> T+F | F is left recursive so / is left associated

so ans of Q1 is d :)

akshat sinha
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