1. Prove that IR2 of the Armstrong Inference Rules is correct (sound). We did that for IR3 in class. Consider F = {BC -> D, B -> E, CE -> D, E -> CA, BF -> G}and R(A,B,C, D,E,F,G) for the next 6 questions. 2. Use all three of Armstrong Rules to "infer" one new FD. 3. Find a minimal cover for F. 4. Find all many keys for R. 5. Find a 3NF decomposition for R that is dependency preserving and has lossless join. 6. Find a BCNF decomposition for R that has lossless join. 7. Apply the lossless join test algorithm on the decomposition of Q6 or the decomposition of Q7 to verif that the decomposition is a lossless join decomposition. You do not need to do that for both Q6 and Q7

Why is an RNN (Recurrent Neural Network) used for machine translation, say translating English to French? (Check all that apply.) It can be trained as a supervised learning problem. It is strictly more powerful than a Convolutional Neural Network (CNN). It is applicable when the input/output is a sequence (e.g. a sequence of words). ⒸRNNs represent the recurrent process of Idea->Code-> Experiment->Idea->....

We wish to build the simplest possible automaton for L = {xcx: x is in (a+b)*}. Note there are two copies of x separated by a special center symbol 'c', e.g., "baacbaa". What is the simplest automaton for deciding L? A. We can decide L using only an NFA. B. We can decide L using a deterministic PDA. C. We need at least a nondeterministic PDA for deciding L. D. We need at least a Turing machine for deciding L.

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