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**gbux512** Im new to proofs, and the proof class i took last semester was absolutely terrible. Im given A isa subset of S and B is a subset of S. I need to prove that a is a subset of the complement of B iff a intersection b = the empty set. i started by breaking it up into two if then statements. I said if a is a subset of the complement of B then a intersect b = the empty set. I have words that prove this, but i cannot figure out how to display this mathematically. I said the intersection of A and B is the set of all elements that are in A and B. Because A is a subset of thej compliment of B, every x in a is also in the compliment of B. because B and the compliment of B share no elements, the intersection of b and a can contain only the null set. Now as far as reversing it and proving the other iff statement I cant even get started. Im sure my other statement is unsatisfactory as well. i feel so confused and demotivated. i wrote down everything important from the book, suck as modus tollens etc as my tool box, but i feel like i have a puzzle with blank pieces, and i cant see how they fit together. any help is appreciated