Let X = {a,b,c,d,e) and T = {X, Ø, {a}, {c,d}, {a,c,d}, {b,c,d,e }} and {A=...
7. Let X = {a,b,c} and T = {x,ø,{a},{b}, {a,b}} be a topological space on X. Let f: X - X be such that f(a) = a, f(b)c and f(c) = b. Is f continuous at a? b? or c?
Let X be a metric space and let E C X. The boundary aE of E is defined by E EnE (a) Prove that DE = E\ E°. Here Eo is the set of all interior points of E; E° is called the interior of E (b) Prove that E is open if and only if EnaE Ø. (c) Prove that E is closed if and only if aE C E (d) For X R find Q (e) For X...
Let L = {w! w can be written as cd#e#c with c, d, e e {a,b}* }. Show that is not regular.
Let R(A,B,C,D,E) be a relation with FDs F = {AB-CD, A-E, C-D, D-E} The decomposition of Rinto R1(A, B, C), R2(B, C, D) and R3(C, D, E) is 2 Points) Select one: Lossless and Dependency Preserving. Lossy and Not Dependency Preserving. Lossless and Not Dependency Preserving. Lossy and Dependency Preserving.
Let R(A,B,C,D,E) be a relation with FDs F = {AB-CD, A-E, C-D, D-E} The decomposition of Rinto R1(A, B, C), R2(B, C, D) and R3(C, D, E) is 2 Points) Select one: Lossless and Dependency Preserving. Lossy and Not Dependency Preserving. Lossless and Not Dependency Preserving. Lossy and Dependency Preserving.
Let X be any set, A C X. Furthermore set T, := {0 € X| A CO}u{@} and Tz:= {0 XANO=Ø}_{x} 17,t, are called the A-inclusion, A-exclusion topology of X, respectively (i) Show that 71,72 are topologies on X. (ii) If A =Ø, then t, = ? and T2 = ? (iii) If A = X, then T, = ? and T2 = ? (iv) Is there any relationship between the two topologies? (i.e. is t, Ct2 or T2 CT,?)...
Let R(A, B, C, D, E) be a relation wit FDs F = {AB->C, CD->E, E->B, CE->A}.... Question 4 Not yet answered Marked out of 2.00 P Flag question Let R(A,B,C,D,E) be a relation with FDs F = {AB-C, CD-E, E-B, CE-A} Consider an instance of this relation that only contains the tuple (1, 1, 2, 2, 3). Which of the following tuples can be inserted into this relation without violating the FD's? (2 points) Select one: 0 (0, 1,...
Let R(A,B,C,D,E) be a relation with FDs F = {AB-CD, A-E, C-D, DE} The decomposition of R into R1(A, B, C), R2(B, C, D) and R3(C, D, E) is (2 Points) Select one: Lossy and Dependency Preserving. Lossless and Not Dependency Preserving. Lossy and Not Dependency Preserving. Lossless and Dependency Preserving.
QUESTION 9 Let X={a,b,c,d), f={(a,b),(6.a),(c,c),(d,d)}cXxX, and g={(a,m),(6,4),(c,b),(d,c)}cXxX. Find fog. a((aa),(b,d),(c,b),(d.c)) b.((a.d),(6.b),(c,a),(d.c)) c. ((a.a),(6.b),(c,c),(d,d)) d.((a.c),(b,d).(c.a),(d.b) QUESTION 10 Let X={a,b,c,d), f={(a,b),(b,a),(c,c),(d,d)}c XXX, and g={(a,d),(b,a),(c,b),(d,c)}cXXX. Find gog. a. ((a.a),(6,d),(c,b),(d,c)} b.([a,d),(6.b),(ca),(d.c)} c.{(a,a),(6.b),(c,c),(d,d)} d.((a.c),(b,d),(c,a),(d,b) QUESTION 11 What is the dominant operation in this algorithm? 1. Input the number of values n 2. Input the list of numbers x1, x2, ..., X 3. min = x 4. For i = 2 to n do 4.1. If xi < min then 4.1.1. min < x; 5. Output...
Consider the relation R with attributes: A, B, C, D, E, and F Let S be a set of functional dependencies in R such that S = { A-> B, CD-> E, C-> D]. Which of these attributes are in the closure of [C, F)?