= Solution
The given <logical implication> is false exactly when $A=B$ and $C\ne D$. For every <literal> on $A,B,C,D$, there is such a false <Boolean valuation> making that <literal> true. For a prescribed value of $A$ or $B$, give the other the same value and choose $C\ne D$. For a prescribed value of $C$ or $D$, give the other the opposite value and choose $A=B$.
Consequently no <literal> implies the whole <propositional formula>: \b[there is no one-<literal> <implicant>]. If an equivalent <disjunctive normal form> contained a one-<literal> conjunction term $\ell$, then every <Boolean valuation> satisfying $\ell$ would satisfy that <disjunctive normal form>, contradicting its equivalence to the given <propositional formula>. This proves the claim. Even if auxiliary <Boolean variables> are allowed in the equivalent expression, a one-<literal> term on one of them fails too: fix any false <Boolean valuation> of the original four and set the auxiliary <literal> true. The word “conjunct” here refers to a conjunction term in the <disjunctive normal form>, not a factor in a <conjunctive normal form>.
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