Show that the set of palindromes over {0, 1} is not regular using the pumping lemma given in Exercise 22. [Hint: Consider strings of form 0N10N]
*22. One important technique used to prove that certain sets not regular is the pumping lemma. The pumping lemma states that if
Trending nowThis is a popular solution!
Chapter 13 Solutions
Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991
- Exercises 7. Express each permutation in Exercise as a product of transpositions. 1. Express each permutation as a product of disjoint cycles and find the orbits of each permutation. a. b. c. d. e. f. g. h.arrow_forwardProve statement d of Theorem 3.9: If G is abelian, (xy)n=xnyn for all integers n.arrow_forward{u1, u2, u3} is an orthonormal set and x = c1u1 + c2u2 + c3u3. ||x|| = 5, <u1,x> = 4 , x ㅗ u2 , find c1,c2,c3arrow_forward
- 7 Determine whether the set {1, x, x²} is linearly dependent dependent in R (Justify your answer !). or in-arrow_forward5 Show that a X-system is a o-algebra if and only if it is a T-system.arrow_forwardIf H is a Hilbert space and SCH, show that s' =st! TT When S is the same as S** ? Justify.arrow_forward
- We have two circuits (Z6, +, ·), (Z12, +, ·). Find out which of the views hi: Z12 → 26, i = 1,2 is the homomorphism of the circuits and then find its kernel, if a) h1 (x) = 2xmod (6) b) h2 (x) = xmod (6)arrow_forwardLet X8 = {1, 2,..., 8}, and let Y8 {b1 b₂b3b4b5 b6b7b8 | bį = {0, 1}} be the set of binary strings of length 8. In lectures, we defined a bijection f : Yg → P(X8). Let 00000000. What is f(b)? b = ○ {8} O 1, 2, 3, 4, 5, 6, 7 00 O X8arrow_forwardLet X = {1,2,3,4}, and consider binary relations R and S, both subsets of X X X, defined defined as follows. (i) R = {(1,1), (1,2), (2,1), (2,2), (4,1)} and (ii) S= R_n{(i,t)\i e X} 1. Precisely list the elements of R-1. Is R a function from X to X (Yes/No and Justify)? How many elements does SX R contain? (Equivalently, find |S X R.) Justify your answer.)arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning