Read the given information carefully and answer the question. In a certain…

Concept

In sentence-substitution coding, each word maps to exactly one code. To pin a word's code, compare statements that share that word: the code common to every statement containing the word, and absent where the word is absent, must be that word's code. Repeatedly applying this intersection-and-elimination logic fixes the codes one by one.

Application

1. ‘the’ is the only word present in all four statements, and ‘ud’ is the only code present in all four. So ‘the’ = ‘ud’.

2. Statement 1 minus ‘the’ gives {play, same, game} = {us, ut, uk}; statement 4 minus ‘the’ gives {same, game, played} = {us, ut, ub}. ‘same’ and ‘game’ are common to both, so they share the codes {us, ut}. The leftover ‘play’ (only in statement 1) = ‘uk’, and ‘played’ (only in statement 4) = ‘ub’.

3. Statement 2 is {seen, in, the, play} = {uk, ua, ud, um}. Removing ‘the’ = ‘ud’ and ‘play’ = ‘uk’ leaves {seen, in} = {ua, um}.

4. Statement 3 is {the, jar, is, seen} = {ud, ua, uh, uw}. ‘seen’ appears here too, so its code must lie in both {ua, um} and {ua, uh, uw}; the only shared code is ‘ua’. Hence ‘seen’ = ‘ua’.

5. Back in statement 2, with ‘seen’ = ‘ua’, the remaining pair forces ‘in’ = ‘um’.

Cross-check

Rebuild statement 2 with the fixed codes: play = uk, seen = ua, the = ud, in = um, which gives exactly ‘uk ua ud um’ — the given code. So ‘um’ stands for ‘in’.