In the problems below, please write formal proofs in column format. You may need to use Hypothesis Introduction, Universal & Existential Instantiation/Generalization.You are also allowed to use rules of propositional logic (if a formula appears on some line, an equivalent formula can appear on the subsequent line); but use them sparingly, only for simple transformations (like double negation or contrapositive)not for long unreadable lines of equivalences, because the whole point of the column format is to make things more readable.

The domain of discourse is sets. Suppose some predicate Q is true for all elements of A: aAQ(a). Recall the definition of subset: XY is defined as bXbY. Suppose B A and C B. Prove that c C Q(c).