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The boolean equation for \$C_o\$ in Full Adder is: $$C_o = A.B + C_i(A+B)$$ Implementing above expression in CMOS logic will give you its complementary version at the output of Full Adder cell: $$\overline{C_o} = \overline{A.B + C_i(A+B)} \tag{1}$$ So you have to add an inverter at the output stage to get \$C_o\$: $$\overline{C_o} \rightarrow \fbox{INVERTER}\...


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If you drew up a truth table for the expression you found, you'd realise that it would exactly the same as the one for the expression they've given you (so you're not wrong). Since you would already have circuitry to find A XOR B (to find S), however, the output of the same circuitry should be re-used to find Cout as shown in the diagram below in order to ...


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