True or false, and justify.
Any subinterval (a,b) ⊂ (0,1) contains a number from the set
D := {1/n | n ∈N}
false
let a =1/2 , b = 1
so interval (a,b)=(1/2,1) ⊂ (0,1)
but ∄ x ∈ D such that x ∉ (1/2,1)
True or false, and justify. Any subinterval (a,b) ⊂ (0,1) contains a number from the set...
3. Consider the Cantor set D formed by deleting the middle subinterval of length 4-* from each remaining interval at step k. (a) Prove that the length of the D is 1/2. Thus D is a fat fractal. (b) What is the box-counting dimension of D? (c) Let be the function of [0,1] which is equal to 1 on D and 0 elsewhere. It is the limit of functions which are Riemann integrable. Note that f is not Riemann integrable....
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...
Determine whether each statement is True or False. Justify each answer. a. A vector is any element of a vector space. Is this statement true or false? O A. True by the definition of a vector space O B. False; not all vectors are elements of a vector space. O C. False; a vector space is any element of a vector. b. If u is a vector in a vector space V, then (-1) is the same as the negative...
Determine whether each statement is True or False. Justify each answer a. A vector is any element of a vector space. Is this statement true or false? O A. False; a vector space is any element of a vector O B. True by the definition of a vector space O C. False; not all vectors are elements of a vector space. b. If u is a vector in a vector space V, then (-1)u is the same as the negative...
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...
TRUE/FALSE (5 points) Answer each of the following as True or False. You don't have to justify your answer. (a) The quotient group Z12/(8) is isomorphic to Za (b) Any subgroup H of G of index 2 is normal in G. (c) For every n 2 2, the quotient group Sn/An is isomorphic to Z2. (d) If H is a normal subgroup of G, then Ha-1H for every a E H (e) The symmetric group S3 has exactly three normal...
Let A be an n×n matrix. Mark each statement as true or false. Justify each answer. a. An n×n determinant is defined by determinants of (n−1)×(n−1) submatrices. b. The (i,j)-cofactor of a matrix A is the matrix obtained by deleting from A its I’th row and j’th column. a. Choose the correct answer below. A. The statement is false. Although determinants of (n−1)×(n−1)submatrices can be used to find n×n determinants,they are not involved in the definition of n×n determinants. B....
3)True or false? ( Justify your answer). a)6sven 6 b)10101wo 2121hree
3)True or false? ( Justify your answer). a)6sven 6 b)10101wo 2121hree
Only 5-9 please
1. (10 points) True/False. Briefly justify your answer for each statement. 1) Any subset of a decidable set is decidable 2) Any subset of a regular language is decidable 3) Any regular language is decidable 4) Any decidable set is context-free 5) There is a recognizable but not decidable language 6) Recognizable sets are closed under complement. 7) Decidable sets are closed under complement. 8) Recognizable sets are closed under union 9) Decidable sets are closed under...
state wether true or false. no need to justify (a) If a sequence is divergent, then it contains two convergent subsequences with distinct limits. (b) If a function f is uniformly continuous on all real numbers, the f is continuous at each b in all real numbers. (c) If a function f^2 is continuous, them so is f continuous. (d) If a differentiable function f on all real numbers satisfies f(0)=-1 and f'(y)>0 for all y>=0, then there is a...