What does it mean to "reproduce Morgan's equivalents along with Boolean Algebra"?
Those are truth tables. And unfortunately they're incomplete. A full truth table with n variables will have 2n rows. The columns on the left are the inputs, and the columns on the right are the outputs. The values of the outputs are determined by both the inputs and the boolean equation for the circuit.

For instance:

Y = AB

A B Y
0 0
0 1
1 0
1 1


becomes:

A B Y
0 0 0
0 1 0
1 0 0
1 1 1