= Solution
\b[No.] The full language can express $\neg(x_0\dot=x_0)$, which is false in the singleton structure from part (i). Every formula of the reduced language is true in that structure under every <assignment in a first-order structure>. Therefore no formula of the reduced language can be logically equivalent to this negated equality.
This is a <singleton truth-preservation obstruction to expressive completeness>. Adding both quantifiers to <logical implication> does not repair the failure: on this particular nonempty singleton model, quantification cannot create a false formula from true <atomic formulas>.
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