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# GATE | GATE-CS-2000 | Question 49

• Difficulty Level : Hard
• Last Updated : 12 Sep, 2019

Given the following expression grammar:

```E -> E * F | F + E | F
F -> F - F | id ```

which of the following is true?
(A) * has higher precedence than +
(B) – has higher precedence than *
(C) + and — have same precedence
(D) + has higher precedence than *

Explanation: Let say i/p is 3*4-5 when we draw parse tree according to grammar

```      E
/  |  \
E   *   F
|     / | \
F    F  -  F
|    |     |
id(3) id(4) id(5)```

As we can see first ‘- ‘ will be evaluated then ‘ * ‘ is evaluated so ‘ – ‘ has higher precedence then *.

So correct choice is B

See question 1 of http://www.geeksforgeeks.org/compilers-set-2/

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