Deepak , I have one doubt.. P=NP implies P ⊆ NP and NP ⊆ P...and P ≠ NP implies P ⊂ NP...So ,I think from these 2 things , we can only say P ⊂ NP..ie. P is a proper subset of NP , not P is subset of NP...
The reason why You got confused is the definition of "Set Equality" which You used i.e. P ⊆ NP and NP ⊆ P
(It is indeed a correct definition) And From this definition and P ⊂ NP, You took what is Common and the common thing that you found was "⊂". But it is wrong. Because What You should have considered was "P ⊆ NP and NP ⊆ P" But You only considered "P ⊆ NP".
There is Nothing common between "Set Equality" and "Proper Subset". Both are Mutually Exclusive and Exhaustive. But The Term "Subset" can be used for Both.