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

Let's analyze the given information step-by-step to determine the birth dates of the eight persons (A, B, C, D, E, F, G, and H).

First, let's list the available months, their number of days, and the dates:
- January (31 days): 5th, 12th
- March (31 days): 5th, 12th
- April (30 days): 5th, 12th
- June (30 days): 5th, 12th

This gives us 8 chronological positions:
1. January 5th (Odd date, 31-day month)
2. January 12th (Even date, 31-day month)
3. March 5th (Odd date, 31-day month)
4. March 12th (Even date, 31-day month)
5. April 5th (Odd date, 30-day month)
6. April 12th (Even date, 30-day month)
7. June 5th (Odd date, 30-day month)
8. June 12th (Even date, 30-day month)

Step 1: Placement of C and F
C was born on an odd date (5th) in a month having an even number of days (April or June).
Therefore, C could be born on April 5th (Position 5) or June 5th (Position 7).
Let's consider these two cases:

Case 1: C was born on April 5th (Position 5)
Three persons were born between C and F. If C is at Position 5, F must be at Position 1 (January 5th) because going forward (5 + 3 + 1 = 9) exceeds the 8 positions.
So, F is at Position 1 (January 5th).
Now, "As many persons were born before F as after B". Since F is at Position 1, there are 0 persons born before F. Thus, there must be 0 persons born after B, which places B at Position 8 (June 12th).
Next, "Four persons were born between D and B". With B at Position 8, counting backwards, D must be at Position 3 (March 5th) (Positions 7, 6, 5, 4 are between them).
Next, "G was born immediately before D". Since D is at Position 3, G must be at Position 2 (January 12th).
So far in Case 1, we have:
1. January 5th: F
2. January 12th: G
3. March 5th: D
4. March 12th: (vacant)
5. April 5th: C
6. April 12th: (vacant)
7. June 5th: (vacant)
8. June 12th: B

Now we have the remaining positions for A, E, and H: Position 4 (March 12th), Position 6 (April 12th), and Position 7 (June 5th).
"A was born on an odd date". The only vacant position with an odd date is Position 7 (June 5th). So, A is at Position 7 (June 5th).
"E was born before H". The remaining vacant positions are Position 4 (March 12th) and Position 6 (April 12th). Since E was born before H, E must be at Position 4 (March 12th) and H must be at Position 6 (April 12th).

Let's check if Case 1 is completely consistent:
1. January 5th: F
2. January 12th: G
3. March 5th: D
4. March 12th: E
5. April 5th: C
6. April 12th: H
7. June 5th: A
8. June 12th: B
All conditions are satisfied perfectly.

Case 2: C was born on June 5th (Position 7)
Three persons were born between C and F. This places F at Position 3 (March 5th).
"As many persons were born before F as after B". Since F is at Position 3, there are 2 persons born before F. Thus, there must be 2 persons born after B, placing B at Position 6 (April 12th).
"Four persons were born between D and B". With B at Position 6, counting backwards to place D is impossible because there are only 5 positions before B. Counting forward is also impossible. Thus, Case 2 is invalid.

Evaluating the Statements using the final arrangement from Case 1:
- Statement I: A was born on 5th June. (True, A is at Position 7, which is June 5th)
- Statement II: E was born after D. (True, E is at Position 4, March 12th, while D is at Position 3, March 5th)
- Statement III: C was born before B. (True, C is at Position 5, April 5th, while B is at Position 8, June 12th)

Therefore, all statements I, II and III are true.