The combinations of the ‘NAND’ gates shown here in fig. are equivalent to

an ‘OR’ gate and an ‘AND’ gate respectively

For first case, $C_1 =\overline{\overline A.\overline B} = (A+ B)$ (by Demorgan's theorem)

The truth table is shown below

This is truth table for $C_1 = A+ B$ i.e. OR gate

For second case, $C_2 = \overline{\overline{A.B}} = A.B$ i.e., AND gate.