Full Adder

Question

The C_out function of a 3-bit adder is as follows:

AB + C_in (A ⊕ B) ----- i

It, being a majority function, can also be written as:

AB+BC_in+C_inA

which is equivalent to

AB + C_in (A+B) ------- ii

So, if we consider eqn i and ii, doesn't it show that (A ⊕ B) = (A+B). What am I missing here?

Comments

Here is how all three equations are the same: