Study the following information carefully and answer the questions given below-

Six persons A, B, C, D, E and F sit around a circular table facing the centre but not necessarily in the same order. They like different flowers viz. Rose, Daisy, Lily, Jasmine, Marigold and Dahila but not necessarily in the same order.

F sits 2nd to the left of the one who likes Rose. B and the one who likes Rose are immediate neighbours. A faces the one who likes Jasmine and sits near F. C sits 2nd to the left of the one who likes Lily. The one who likes Dahila sits just right of the one who likes Daisy. C and D are not an immediate neighbour.

Which of the following is true?
I. D and F are not an immediate neighbour
II. A likes Lily
III. D does not like Rose

Let's analyze the given information step-by-step to determine the positions of the six persons (A, B, C, D, E, F) and the flowers they like (Rose, Daisy, Lily, Jasmine, Marigold, Dahlia).

Step 1: Analyze the circular arrangement constraints:
- Six persons sit around a circular table facing the centre.
- "F sits 2nd to the left of the one who likes Rose." Let's place the person who likes Rose at position 1. Since F is 2nd to the left of this person, and they face the centre, F will be at position 5 (moving clockwise).
- "B and the one who likes Rose are immediate neighbours." Therefore, B can be at position 2 or position 6.
- "A faces the one who likes Jasmine and sits near F." Since A sits near F, A must be adjacent to F. A can be at position 4 or position 6. A faces the person directly opposite to him/her (since there are 6 people, the person opposite to position $x$ is $x+3$ or $x-3$). So the person opposite to A likes Jasmine.
- "C and D are not immediate neighbours."
- "C sits 2nd to the left of the one who likes Lily."
- "The one who likes Dahlia sits just right of the one who likes Daisy."

Step 2: Testing cases:
Let the positions be 1 to 6 in clockwise order.
Let Person at 1 like Rose.
F is at 5 (2nd to the left of 1).
A must be adjacent to F, so A is at 4 or 6.
Also, A faces the one who likes Jasmine. The opposite of 4 is 1, and the opposite of 6 is 3.
If A is at 4, the person opposite to A is at 1, who likes Rose. But the person opposite to A must like Jasmine. This is a contradiction. Therefore, A must be at position 6.
Since A is at position 6, the person opposite to A (position 3) likes Jasmine.
Since A is at position 6, and B must be an immediate neighbour of the one who likes Rose (position 1), B could be at 2 or 6. Since A is already at 6, B must be at position 2.

Step 3: Determining positions of C, D and E:
We have the following layout so far:
- Position 1: Likes Rose. (Occupied by C, D, or E)
- Position 2: B.
- Position 3: Likes Jasmine. (Occupied by C, D, or E)
- Position 4: (Occupied by C, D, or E)
- Position 5: F.
- Position 6: A.
Now, "C and D are not immediate neighbours."
The remaining positions for C, D, and E are 1, 3, and 4.
Since C and D cannot be adjacent, and positions 3 and 4 are adjacent, C and D cannot occupy 3 and 4. One of them must occupy position 1, and the other must occupy position 3 or 4, but they cannot be next to each other. Let's test the possibilities:
- If D is at 1 and C is at 3, they are not immediate neighbours (B is at 2, separating them). If C is at 3, D is at 1, then E must be at 4.
- If C is at 1 and D is at 3, they are separated by B. Then E is at 4.
- If C is at 1 and D is at 4, they are not adjacent. Then E is at 3.
- If D is at 1 and C is at 4, they are not adjacent. Then E is at 3.

Step 4: Use flower clues:
"C sits 2nd to the left of the one who likes Lily."
This means the person C is 2nd to the left of the person with Lily. In our 6-position circle, C is at position $p$ and the Lily-lover is at position $p+2$ (counter-clockwise/left from Lily-lover is clockwise, so Lily-lover is at $p+2$ in clockwise direction).
Let's test C's position:
- If C is at 1: Lily-lover is at 3. But position 3 likes Jasmine. This is a contradiction.
- If C is at 3: Lily-lover is at 5 (which is F). But C cannot be at 3 if Lily-lover is at 5. Let's check: 2nd to the left of 5 (F) is 3 (C). This works! So C is at 3, and F (at 5) likes Lily. But wait, if C is at 3, then D cannot be at 4 (since C and D are not immediate neighbours), so D must be at 1. Then E is at 4.
- If C is at 4: Lily-lover is at 6 (which is A). So A likes Lily. Let's check: 2nd to the left of 6 (A) is 4 (C). This also works!
Let's analyze this case: A (at 6) likes Lily. Since C is at 4, D cannot be at 3 (adjacent to 4) and cannot be at 5 (occupied by F). So D must be at 1. Since D is at 1, E must be at 3.
Let's write down this arrangement:
- Position 1: D (likes Rose)
- Position 2: B
- Position 3: E (likes Jasmine)
- Position 4: C
- Position 5: F
- Position 6: A (likes Lily)
Now we check the remaining flower clue: "The one who likes Dahlia sits just right of the one who likes Daisy."
Let's see the remaining flowers for B, C, D, E, F, A. We know: D likes Rose, E likes Jasmine, A likes Lily. The remaining flowers are Daisy, Dahlia, and Marigold.
"Dahlia sits just right of Daisy." Since facing the centre, "just right" means adjacent in the counter-clockwise direction.
We need two adjacent positions for Daisy and Dahlia. The remaining positions with unknown flowers are 2 (B), 4 (C), and 5 (F).
Positions 4 and 5 are adjacent. So, Daisy can be at 4 (C) and Dahlia at 5 (F) (since F at 5 is to the immediate right of C at 4, facing the centre).
This perfectly fits! The remaining person B at position 2 likes Marigold.
Let's verify all conditions:
- F (5, Lily) sits 2nd to the left of Rose (1, D). Correct.
- B (2) and Rose (1, D) are immediate neighbours. Correct.
- A (6) faces the one who likes Jasmine (3, E) and sits near F (5). Correct.
- C (4) sits 2nd to the left of Lily (6, A). Correct.
- The one who likes Dahlia (5, F) sits just right of the one who likes Daisy (4, C). Correct.
- C (4) and D (1) are not immediate neighbours. Correct.

Step 5: Evaluate the statements:
- I. D and F are not an immediate neighbour: D is at position 1 and F is at position 5. Their neighbours are (6, 2) and (4, 6) respectively. They are not immediate neighbours. Thus, Statement I is true.
- II. A likes Lily: From our derivation, A is at position 6 and likes Lily. Thus, Statement II is true.
- III. D does not like Rose: From our derivation, D likes Rose. Thus, Statement III is false.

Therefore, both Statement I and Statement II are true.