[unspun]

{a} is a subset of the set {a + b}.

{a + b} cannot be said to be of {a}.

But {a + b} while not being *of* {a} may be in {a} just as it is in {b}, since {a} is a subset of {a + b}.

[LogicWings]

But {a + b} while not being *of* {a} may be in {a} just as it is in {b}, since {a} is a subset of {a + b}.

No, this is wrong. {a + b} may NOT be in {a}. You are playing fast and loose with definitions here.

Water contains oxygen but no oxygen contains water just because water is made up of oxygen and hydrogen, which your lousy algebra says here. As I said, you need to go study logic for a good long while, you just don't get it.