Obtain grammar to generate strings of a’s and b’s such that string length is multiple of three.

Sure, here is a context-free grammar that generates strings of a's and b's such that the string length is a multiple of three:

1. S -> aaa | bbb | aSa | bSb | ε

Here is a step-by-step explanation:

1. The non-terminal symbol S represents a string whose length is a multiple of three.
2. The production rule S -> aaa generates a string of three a's.
3. The production rule S -> bbb generates a string of three b's.
4. The production rule S -> aSa generates a string whose length is a multiple of three, by adding an 'a' at the beginning and end of any string generated by S.
5. The production rule S -> bSb generates a string whose length is a multiple of three, by adding a 'b' at the beginning and end of any string generated by S.
6. The production rule S -> ε generates an empty string, which has a length of zero (a multiple of three).

This grammar can generate all strings of a's and b's whose length is a multiple of three, and only those strings.