ANSWER TO MOCK QUESTION 3:

(i) satisfiable (A=emp), but invalid (A=x↦2).

(ii) satisfiable (x=y), but invalid (x≠y)

(iii) unsatisfiable. For any value v of x, heaps {v↦2} and {v↦2} are not disjoint)

(iv) valid. Proof below.

(v) satisfiable (A=emp), but invalid. Take A= x↦2 ∨ y↦3; B= x↦2; C= y↦3. 
    Then heap {x↦2, y↦3} satisfies LHS, but no heap satisfies RHS
    since B∧C is false.

(vi) satisfiable (C=emp), but invalid. Take A= true, B= x↦2, C=x↦2. 
     The heap {x↦2} satisfies A⇒B, and it satisfies A*C, but it
     doesn't satisfy B*C, which is false.

Proof of (iv):

Suppose s,h ⊧ A*B ∨ A*C.
Then s,h ⊧ A*B or s,h ⊧ A*C.
So ∃h1 h2. h = h1+h2 ∧ s,h1⊧A ∧ s,h2⊧B
or ∃h1 h2. h = h1+h2 ∧ s,h1⊧A ∧ s,h2⊧C
Hence (since "or" distributes over ∃):
∃h1 h2. (h = h1+h2 ∧ s,h1⊧A ∧ s,h2⊧B) ∨ (h = h1+h2 ∧ s,h1⊧A ∧ s,h2⊧C)
Hence: ∃h1 h2. h = h1+h2 ∧ s,h1⊧A ∧ (s,h2⊧B ∨ s,h2⊧C)
Hence: ∃h1 h2. h = h1+h2 ∧ s,h1⊧A ∧ s,h2⊧B∨C
Hence: s,h ⊧ A * (B∨C) as required.