Question: ( c ) Let A and B be propositional formulae. Let U be a set of propositional formulae. Are the following statements always correct? Whenever

(c) Let A and B be propositional formulae. Let U be a set of propositional
formulae. Are the following statements always correct? Whenever they are,
prove this. When a statement is incorrect, provide a counterexample.
(i) If A is valid, then so is A B.
(ii) If A B is falsifiable, then A is satisfiable.
(iii) If U is unsatisfiable, then so is U \cup {A}.

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