The general formula  ${\mathrm{C}}_{\mathrm{n}}{\mathrm{H}}_{2\mathrm{n}-2}$ is true for

[Step 1]:
Alkyne is an open chain unsaturated hydrocarbon. It contains one triple bond  between carbon and carbon atoms. Therefore four hydrogen atoms are relatively less   than alkane.
[Step 2]:
Alkadiene is an open chain unsaturated hydrocarbon. It contains two double bonds.  Therefore four hydrogen atoms are relatively less than alkane. 
[Step 3]:
Cyclo alkene is a ring chain compound having one double bond. Due to cyclic form  two hydrogen’s and presence of one double bond two hydrogens, total four  hydrogens are relatively less than  alkane.