"And" requires that BOTH parts be present for it to be true.
"And" is not the same thing as "or."
If x is red and blue then you can't argue that x is ONLY blue without violating the boolean logic of "and".
Quite true, friend. This is called a formulistic argument that has CLEAR merit in many
situations. However, allow me to sprinkle a dash of realistic argument to the formula to illustrate:
Therefore, under your just-made-point: an economy that allowed complete ownership of production, but then took complete control of the administration of distribution would NOT be socialist? Or vis versa.
In application: Government requires all car manufacturers to surrender all dealership licenses to itself as the only authorized distributor. (This hypo could easily include used-car market AND the private party car market, as under your understanding it can only be socialist if the government has ownership AND administration.) Even if you "owned" a used car, you could not sell it to anyone since it's use could be "administered" through regulation. That about right?
Under that logic China is not a socialist system. Since China honors private ownership, production, etc. Not socialist at all that place.