Step 1: Understand meiosis prophase-I.
Prophase-I of meiosis is divided into five substages.
These are:
\[
\text{Leptotene, Zygotene, Pachytene, Diplotene and Diakinesis}
\]
During these stages, homologous chromosomes pair, exchange segments and then prepare for separation.
Step 2: Understand desynapsis.
Synapsis is the pairing of homologous chromosomes.
Desynapsis means separation of homologous chromosomes after crossing over.
It begins during diplotene and continues toward diakinesis.
Thus, desynapsis is completed by diakinesis.
Therefore,
\[
\text{Statement 1 is true.}
\]
Step 3: Understand terminalisation.
During diakinesis, chiasmata move toward the ends of chromosomes.
This movement of chiasmata toward terminal ends is called terminalisation.
Diakinesis is mainly characterized by terminalisation of chiasmata, condensation of chromosomes and disappearance of nucleolus.
Therefore,
\[
\text{Statement 2 is true.}
\]
Step 4: Final conclusion.
Since both statements are correct, the correct answer is
\[
\boxed{\text{Statement 1 and statement 2 are true}}
\]