(1) Please show that each of the followings is not  a valid rule about FD’s by giving a counter example. (Note that you are allowed to use only (a and b) two symbols to construct your tuples.) (a) If AB→C and A→C, then B→C. (b) If AB→C, then A→C or B→C.

This distinction between function and relation regarding the classification of deterministic and nondeterministic devices fascinates me.

WRITE CFG TO CNF(Chomsky Normal Form) ?

Determine which of these relations are reflexive. The variables x,y,x',y' represent integers. A. x~y if and only if x+y is even B. x~y if and only if x+y is odd C. x~y if and only if x+y is positive D. x~y if and only if xy is positive E. x~y if and only if x-y is a multiple of 10

The comparison of deterministic versus non-deterministic computers, which are focused on function rather than relation, piques my interest.

Question 2) form. Show all your work STEP by STEP. Explain the steps and apply the required changes until the normal form is achieved. Convert the following CFG to an equivalent CFG in Chomsky normal S→ AB JABC |aS A → aA E > bB C cC c В C

7. Put the rules following in Chomsky normal form (assume that S is the new start variable) S → aAA | aBC | abc A → AA | Aa | ab B — aaBC | BC C →a | bc

answer the following boxes

1) Consider the following relation instance of R1(A, B, C) contains the tuples {(a1,b1.c1). (a2,b1,c1), (a3,b3,c3), (a4,b3,c3), (a5,b5.c5). (a6,b6,c6)} and S1(B, C, D, E) contains the tuples ((b1.c1,d1,e1), (b1.c1.d2.e2),.(b1.c1,d3,e3), (b2.c2,d2.e2), (b3,c3,d4,e4).(b6.c7.d8,e9)) The following SQL query will result in how many tuples? Select From R1 r LEFT OUTER JOIN S1 s (ON r.B= s.B AND r.C=s.C): (The answer will simply be an integer, like 25). Answer: 2) Consider a relation schema R = (A, B, C, D, E, F, G} with the following set of functional dependencies: F = (BG A, CGA, A BC, BC A, BD E, EF, CF B) The decomposition of R into R1 = (A, B, C, G), R2 = {B, D, E), R3 = (B, C, F) and R4 = (E, F) is O In BCNF but Not in 3NF. In 3NF but Not in BCNF. In 3NF and in BCNF. Not in 3NF and Not in BCNF 3)

Electrical connectivity is an example of equivalence relation.a) trueb) false