The question asks us to identify the digit that represents the word 'and' based on a given code language.

Decoding the Code Language

We are given three coded phrases:

• '273' means 'they bought vegetables'
• '784' means 'fruits and vegetables'
• '128' means 'I bought fruits'

Step-by-Step Analysis

1. Compare Phrase 1 and Phrase 3:
   • '273' = 'they bought vegetables'
   • '128' = 'I bought fruits'
   The common digit is '2'. The common word is 'bought'. Therefore, '2' represents 'bought'.
2. Compare Phrase 1 and Phrase 2:
   • '273' = 'they bought vegetables'
   • '784' = 'fruits and vegetables'
   The common digit is '7'. The common word is 'vegetables'. Therefore, '7' represents 'vegetables'.
3. Analyze Phrase 2:
   • '784' = 'fruits and vegetables'
   We know '7' represents 'vegetables'. The remaining digits are '8' and '4', and the remaining words are 'fruits' and 'and'. So, {'8', '4'} corresponds to {'fruits', 'and'}.
4. Compare Phrase 2 and Phrase 3:
   • '784' = 'fruits and vegetables'
   • '128' = 'I bought fruits'
   The common digit is '8'. The common word is 'fruits'. Therefore, '8' represents 'fruits'.
5. Final Deduction for 'and': From Step 3, we established that {'8', '4'} represents {'fruits', 'and'}. Since we now know '8' represents 'fruits' (from Step 4), the remaining digit '4' must represent the word 'and'.

Conclusion

The digit representing 'and' is 4.