1. (32 points) Please answer the following questions by circling the correspondi

Question

1. (32 points) Please answer the following questions by circling the corresponding letter TTuE or F(False). (a) A tuple variable is not bound if it is quantified. TF T F (c) not(V x)(P(x) (not )(P(x) T F (d) SQL does not allow a table (relation) to have two or more tuples that sre identical in al their attribute values. T F (e) The SQL set operations apply only to Union compatible relations. T F (f) A set of attributes X functionally determines a set of attributes Y if the value of X deter- TF mines some values of Y. (g) Armstrong's inference rule for Functional Dependencies (FD): If Y C X, then X ? Y. T F (b) Inference Rule for Functional Dependencies (FD): If X ? YZ, then X ? Y or X- TF

Explanation / Answer

a) FALSE because a tuple is not bound if it is not quantified .

b) TRUE because if the predicate is true for all values of x then obviously it will be true for some values of x.

c) FALSE because if we take the r.h.s we can write it as = not(not forall(x) ( not P(x)) = forall(x) (not P(x)).Now if some values of P(x) is true and some values is false then l.h.s is true and r.h.s is false.So, this is false.

d) FALSE sql allows two or more tuples to be same because it works on multiset.

e) TRUE

f) FALSE as X should determine all values of Y.

g) TRUE

h) FALSE as if X->YZ then X->Y and X->Z.

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