Step 1: Set the scene.
Stars are born inside large clouds of gas and dust called nebulae, so we trace the early steps of star birth.
Step 2: Check Statement-I.
The gas in a nebula is not spread evenly; it clumps into denser, localised lumps. So Statement-I is correct.
Step 3: Check Statement-II.
Inside each lump gravity pulls the gas inward, packing it more tightly until a dense central core forms. So Statement-II is correct.
Step 4: See how they link.
The lumps of Statement-I are exactly where the cores of Statement-II grow, so the two ideas follow one after the other.
Step 5: Decide truth values.
Both statements describe real and correct stages of star formation.
Step 6: Conclude.
Both statements are correct.
\[ \boxed{\text{Both statement-I and statement-II are correct}} \]