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

To determine which of the statements are true, let us analyze the given information step-by-step to reconstruct the seating arrangement and flower preferences of the six persons (A, B, C, D, E, and F) sitting around a circular table facing the centre.

Let the six positions around the circular table be numbered 1 to 6 in a clockwise direction. Since they face the centre, "left" refers to a clockwise direction and "right" refers to an anticlockwise direction.

Step 1: Placement of F and the Rose lover
Let us place the person who likes Rose at position 1.
F sits 2nd to the left of the one who likes Rose. In a circular arrangement of 6 people, 2nd to the left of position 1 is position 3 (moving clockwise).
So, F is at position 3, and the person at position 1 likes Rose.

Step 2: Placement of B
B and the one who likes Rose (position 1) are immediate neighbours. This means B can be at position 2 or position 6.
Let us keep these two possibilities in mind.

Step 3: Placement of A and the Jasmine lover
We are told: "A faces the one who likes Jasmine and sits near F."
Since F is at position 3, the immediate neighbours of F are positions 2 and 4. Thus, A must be at either position 2 or position 4.
Also, A faces the one who likes Jasmine. In a 6-person circle, the position opposite to position 2 is position 5, and the position opposite to position 4 is position 1.
Let's analyze the two cases for A:
- Case A: A is at position 4.
If A is at position 4, then the person opposite to A is at position 1. Therefore, the person at position 1 must like Jasmine. However, we already know the person at position 1 likes Rose. This is a contradiction. Thus, A cannot be at position 4.
- Case B: A is at position 2.
Therefore, A must be at position 2. The person opposite to A is at position 5, which means the person at position 5 likes Jasmine.
Since B must be a neighbour of position 1, and position 2 is occupied by A, B must be at position 6.

Let's summarize the positions and preferences so far:
- Position 1: Likes Rose (Person: unknown)
- Position 2: A (Flower: unknown)
- Position 3: F (Flower: unknown)
- Position 4: (Person: unknown, Flower: unknown)
- Position 5: Likes Jasmine (Person: unknown)
- Position 6: B (Flower: unknown)

Step 4: Placement of C and D
We are told "C and D are not immediate neighbours."
The remaining empty positions for persons are 1, 4, and 5.
If we place C and D in these positions, we must ensure they are not adjacent. The adjacent pairs among these are (6,1), (1,2), (3,4), (4,5), (5,6). Specifically, position 4 is adjacent to position 3 (F) and position 5. Position 5 is adjacent to position 6 (B) and position 4. Position 1 is adjacent to position 6 (B) and position 2 (A).
Let's look at the adjacency of the empty spots (1, 4, 5):
- Position 4 is adjacent to position 5. So C and D cannot occupy positions 4 and 5 simultaneously.
Therefore, one of C or D must occupy position 1, and the other must occupy either position 4 or 5 (but not both).
Since C and D are at position 1 and position 4/5, the remaining position among 1, 4, and 5 must be occupied by E.
Let's look at the clue: "C sits 2nd to the left of the one who likes Lily."
This means: (Position of C) = (Position of Lily lover) + 2 (in clockwise direction).
Equivalently, the Lily lover sits 2nd to the right of C (anticlockwise).
Let's test the possible positions for C (which are 1, 4, or 5):
- Sub-case 1: C is at position 1.
If C is at position 1, the Lily lover must be at position 5 (since 1 + 4 = 5, or 2 positions anticlockwise from 1 is 5). But position 5 likes Jasmine, not Lily. Contradiction.
- Sub-case 2: C is at position 5.
If C is at position 5, the Lily lover must be at position 3. Since F is at position 3, F would like Lily.
Since C is at position 5, D cannot be at position 4 (as C and D are not immediate neighbours). Thus, D must be at position 1.
This leaves E to be at position 4.
Let's check if this is consistent:
- Position 1: D (likes Rose)
- Position 2: A (likes Lily? Let's check below)
- Position 3: F (Flower: unknown, but let's check)
Wait, if C is at position 5, the Lily lover is at position 3 (F). Let's see if this matches the options. Option II says "A likes Lily". If A is at position 2, and the Lily lover is at position 3, then F likes Lily, not A. Let's check the other sub-case.
- Sub-case 3: C is at position 4.
If C is at position 4, the Lily lover must be at position 2. Since A is at position 2, A likes Lily. This matches statement II perfectly!
Since C is at position 4, D cannot be at position 5 (since 4 and 5 are adjacent). Thus, D must be at position 1 (who likes Rose). Wait! If D is at position 1, then D likes Rose. But statement III says "D does not like Rose". Let's check if there is another configuration or if we made an error in direction.
Let's re-verify: "C sits 2nd to the left of the one who likes Lily."
Facing the centre: left is clockwise. So if Lily lover is at X, C is at X + 2 (clockwise).
If Lily lover is at position 2 (A):
1 (Rose), 2 (Lily), 3 (F), 4 (C), 5 (Jasmine), 6 (B).
C is at position 4. 2nd to the left of Lily (position 2) is indeed position 4 (since 2 + 2 = 4). This matches.
If C is at 4, D cannot be at 5 (adjacent). So D must be at 1. Since D is at 1, D likes Rose. This means Statement III ("D does not like Rose") is FALSE, which means Statement I ("D and F are not an immediate neighbour") and Statement II ("A likes Lily") are TRUE.
Let us check the adjacency of D (position 1) and F (position 3). Since they are at positions 1 and 3, they are not immediate neighbours (separated by position 2, A). Thus, Statement I is TRUE.
Since A is at position 2, A likes Lily. Thus, Statement II is TRUE.<>

Therefore, both statements I and II are true.