Let (N,*) where a,b, c € N; a * b = lcm[a, b]a) It is * a law of internal composition in N?b) It is * associative in N?c) Has identity * in N?d) It is * commutative in N?

Given : ℕ, * be the algebraic structure such that a*b = lcm[a, b], where a, b ∈ℕ. To check :…

Answered: Let (N,*) where a, b, c E N; a * b =…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Discrete math
Consider the following definitions for sets of characters:•Digits ={0,1,2,3,4,5,6,7,8,9}•Letters ={a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z}•Special characters ={∗,&,$,#}Compute the number of passwords that satisfy the given constraints.(i) Strings of length 7. Characters can be special characters, digits, or letters, with no repeated characters.(ii) Strings of length 6. Characters can be special characters, digits, or letters, with no repeated characters. The first character can not be a special character.
prove that (1, 6) 13 an o pen set 13 an open çet.

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Let (N,*) where a, b, c E N; a * b = lcm[a, b] a) It is a law of internal composition in N? b) It is associative in N? c) Has identity* in N? d) It is* commutative in N?

Let (N,) where a, b, c E N; a b = lcm[a, b] a) It is a law of internal composition in N? b) It is associative in N? c) Has identity* in N? d) It is* commutative in N?