Eight persons — A, B, C, D, E, F, G and H — were born on two different dates i.e. 5th and 12th of four different months viz. January, March, April and June of the same year. No two persons were born on the same day.

C was born on an odd date in the month having even number of days. Three persons were born between C and F. As many persons were born before F as after B. Four persons were born between D and B. G was born immediately before D. A was born on an odd date. E was born before H.

Which of the following statements is/are true?
I. A was born on 5th June
II. E was born after D
III. C was born before B

To determine which of the statements are true, let us organize the given information step-by-step to construct the birth schedule of the eight persons.

First, we list the months along with the number of days they contain, and the two possible dates (5th and 12th) in chronological order:
1. January (31 days) — 5th January
2. January (31 days) — 12th January
3. March (31 days) — 5th March
4. March (31 days) — 12th March
5. April (30 days) — 5th April
6. April (30 days) — 12th April
7. June (30 days) — 5th June
8. June (30 days) — 12th June

Step 1: Locate C and F
According to the clues, C was born on an odd date (5th) in a month having an even number of days. The months with 30 days are April and June. Therefore, C must be born on either 5th April or 5th June.
Let us analyze these two cases:

Case 1: C was born on 5th April (Position 5)
Three persons were born between C and F. Counting backwards from Position 5, F must be born on 5th January (Position 1).
As many persons were born before F as after B. Since 0 persons were born before F (Position 1), 0 persons must be born after B, which means B was born on 12th June (Position 8).
Four persons were born between D and B. Since B is at Position 8, counting 4 positions back (7, 6, 5, 4), D must be at Position 3, which is 5th March.
G was born immediately before D. Since D is at Position 3, G must be born on 12th January (Position 2).
A was born on an odd date. The remaining vacant slots are Position 4 (12th March), Position 6 (12th April), and Position 7 (5th June). The only remaining slot with an odd date is Position 7, so A must be born on 5th June.
E was born before H. The remaining vacant slots are Position 4 (12th March) and Position 6 (12th April). Since E was born before H, E must be at Position 4 (12th March) and H must be at Position 6 (12th April).

This gives us the following complete arrangement for Case 1:
1. 5th January — F
2. 12th January — G
3. 5th March — D
4. 12th March — E
5. 5th April — C
6. 12th April — H
7. 5th June — A
8. 12th June — B

Case 2: C was born on 5th June (Position 7)
Three persons were born between C and F. Counting backwards, F must be born on 5th March (Position 3).
As many persons were born before F (2 persons: 5th Jan and 12th Jan) as after B. Therefore, 2 persons were born after B, placing B on 12th April (Position 6).
Four persons were born between D and B. Since B is at Position 6, D must be born on 5th January (Position 1).
G was born immediately before D. However, D is at Position 1, so no one can be born before D. Thus, Case 2 is invalid.

Evaluating the Statements:
Based on the valid arrangement from Case 1:
I. A was born on 5th June: True (A is at Position 7).
II. E was born after D: True (E was born on 12th March, while D was born on 5th March).
III. C was born before B: True (C was born on 5th April, while B was born on 12th June).

Since all statements I, II, and III are true, the correct option is All I, II and III.