Study the following information carefully and answer the questions given…

Concept

A linear birth-order puzzle is solved by fixing positions along a single timeline. Order the six possible birth slots chronologically first (month, then date within month), then translate every clue — "immediately before", "two persons before", "born between", "odd/even date", "month with even/odd number of days" — into a position relation on that timeline. "Born before" means an earlier slot; "X persons born between" means the two positions are X+1 apart.

Setting up the timeline

Months April (30 days, even), July (31 days, odd) and September (30 days, even), each on the 9th (odd date) and 26th (even date) of the same year, give six slots from earliest to latest:

1. April 9 (odd date)

2. April 26 (even date)

3. July 9 (odd date)

4. July 26 (even date)

5. September 9 (odd date)

6. September 26 (even date)

Applying the clues

• "D was born immediately before F, on an odd date, in a month with an even number of days" — an even-days month is April or September, so D could initially be April 9 or September 9 (both are odd dates immediately followed by another slot). Testing the September-9 branch against the next clue shows it fails (below), so D = April 9 and F = April 26 is the branch that survives.

• "E was born immediately before C on an even date" — testing this against the September-9 branch for D: the only even-date slots left there are April 26 and July 26, but placing E at either forces E onto the yellow slot later, which contradicts "E doesn’t like yellow" — so the September-9 branch is eliminated, confirming D = April 9. With April taken by D and F, E = July 26 and C = September 9.

• "The one who likes pink was born two persons before C" — two slots before C (September 9) is July 9, so that person likes pink.

• "A was born two persons after the one who likes yellow and before the one who likes green" — placing A at July 9 makes A like pink, yellow two slots earlier at April 9, and green still ahead of A.

• "Two persons were born between F and the one who likes red" — three slots from F (April 26) lands on September 9, so C likes red.

• "Two persons were born between pink and blue" — three slots from pink (July 9) is September 26, which likes blue; the remaining person B sits there, and the leftover person at April 26 (F) likes white, July 26 (E) likes green.

Final arrangement

Checking each statement

• Statement I — "C was born before D": C is at September 9 while D is at April 9, so C is actually the later of the two. The claim is false, so this statement is incorrect.

• Statement II — "No person was born between F and the one who likes pink": F is at April 26 and pink is at July 9, which are consecutive slots, so indeed nobody lies between them. The claim is true, so this statement is correct.

• Statement III — "E was born in the month with an odd number of days and likes green": E is at July 26; July has 31 days (odd) and E likes green. Both parts hold, so this statement is correct.

Result

Only statement I is incorrect, so the set of incorrect statements is exactly {I}.