number 6 a until h 6. In the following questions suppose A -(a, b, c). Assume...
1. Let A be the set {e, f, g, h} and B be the set {e, g, h}. a. Is A a subset of B? b. Is B a subset of A? c. What is A Ս B? d. What is A x B? e. What is the power set of B? 2. Determine whether these statements are true or false? a. ∅ ∈ {∅} b. {∅} ∈ {∅} c. {∅} ⊂ {∅, {∅}} d. ∅ ∈ {∅, {∅}} e....
For the following items, suppose A la,b,e,e Mark the statement TRUE or FALSE. If the statement is FALSE, then modify it to make it true c. ØeP(B)
17-26 true or false questions 17. The smallest positive real number is c, where c = card(0,1). 18. To show that two sets A and B are equal, show that x A and x B. 19. If (vx)P(e) is false, then P(x) is never true for that domain. 20. If R is a relation on A and if (a, a) is true for some a in A, then R is reflexive. 21. If f:A → B is a function, then...
6.2.24 Justify each Assume all vectors are in R. Mark each statement True or False. Justify each answer a. Not every orthogonal set in Rn is linearly independent. O A. False. Orthogonal sets must be linearly independent in order to be orthogonal. O B. True. Every orthogonal set of nonzero vectors is linearly independent, but not every orthogonal set is linearly independent. O C. False. Every orthogonal set of nonzero vectors is linearly independent and zero vectors cannot exist in...
6. In the questions below, suppose A = {a, b, d} and B = {a, b, {d}}. a. [5 pts] Is A B.? Make sure to justify your answer. b. [5 pts] Find the power set of A: P (A)
(b) Is the following statement true for all sets A and B? P(A) UP(B) CP(AUB). If it is, give a proof and, if not, provide a counterexample. (Recall that P(X) denotes the power set of X.)
Analysis of Algorithms Fall 2013 Do any (4) out of the following (5) problems 1. Assume n-3t is a power of 3 fork20. Solve accurately the following recursion. If you cannot find the exact solution, use the big-O notation. Tu) T(n)Tin/3)+2 2. Suppose that you have 2 differeut algorithms to solve a giveu probleen Algorithm A has worst-case time complexity e(n2) and Algorithm B has worst-case time complexity e(nlog n). Which of the following statements are true and which are...
Suppose R is a one-to-one relationship from R1 = { a, b, c, d; to R2 = {e, f, g, h} of the following sets, which one is NOT a valid instance of R? (2 points) Select one: f), the empty set. {(cg)} {(a, e) (b,f).(b,9)} {(ah), (b, g),c, f), (d, e)} All of the above None of the above.
Suppose R is a one-to-one relationship from R1 = { a, b, c, d} to R2 = {e, f, g, h}. Of the following sets, which one is NOT a valid instance of R? (2 points) Select one: о 1, the empty set O {(c, g)} {(a, e),(6,1),(6,9)} {(a,h), (0.9), (C, f), (d, e)}. All of the above. None of the above.
I want to know the answer and explanation of (d) and (f). 2. Percentiles and Quartiles Given a data set with n data values yvi < /2 ..S yn, define the pth percentile of the data set to be the element at index ceiling, and it means that we always round up to the next integer. For example, suppose we have a data set with n - 13 elements, and we want to calculate the 25th percentile of the data...