If a ⊂ b and a ∩ b = θ then which of the following can be concluded about the sets a and b?
set a has more elements in it than set b.
set a is the set containing zero.
set a is the empty set.
both sets a and b are the empty set.

 A ⊂ B means all of A is in B

but then it says A ∩ B = θ meaning they have nothing in common, ie, none of A is in B or vice versa

A must be the empty set for both these conditions to hold. B could be anything you want. B could be empty, or it could not be. It's impossible to tell. 

For certain, A must be empty. Which is why the answer is choice C