How to find NAND logic with the help of full adder?
to design a Logic circuit with nand gates you need your equations in the form of a Sum of products, the equation for C is in the form you need, but the S equation is not, you need to expand the equation to get the desired form:
S = C’(x+y+z)+xy
S = C’x+C’y+C’z+xy

Now that you have the equations in the form you want you proceed to design the circuit having in mind that a plus in the equation is a logic OR gate and that a multiplication is an AND gate.
Now as the equations are in the form of sum of products, you can use NAND gates instead of AND gates, OR gates, and Logic Inverters.
This is the Final Circuit and the time table
Circuit with AND and OR gates:

Circuit with NAND gates:

Time Table: