Which of the following statements are correct with regard to business cycles?

$[1]$ A trough refers to the turning point in the business cycle, before the upswing starts.

$[2]$ A peak refers to the turning point in the business cycle, where the downswing ends.

$[3]$ The upswing of the business cycle refers to the period when production in the economy is increasing.

$[4]$ The downswing in the business cycle refers to the period when the economy is in an expansionary phase.

Select one:

a$.$ only $1$ is correct

b$.$ only $2$ and $4$ are correct

c$.$ only $1,2$ and $3$ are correct

d$.$ only $4$ is correct

e$.$ only $3$ is correct

f$.$ only $1,2$ and $4$ are correct

g$.$ only $1$ and $4$ are correct

h$.$ none are correct

i$.$ only $1$ and $3$ are correct