Question

discrete math

a. For the finite state automaton given by the transition diagram, find the states, the input symbols, the initial state, the accepting states and write the annotated next-state table (inspired by Johnsonbaugh, 1997, p. 560). (4 marks) 02 (Johnsonbaugh, 1997, p. 560)

Answer 1

06 n To select a comitte of K people with the president К" К combinatie kon! Klink)! of group of Becaine I have expanded this far n. (nl) (k-1)} (n-K)} n people you com. 1. Select the k commitee members and then select the president from the members 2. Select the president from the in people and the Kl remaining members from the remaining (nt) people Left side k (BJ = khi K!(n-k)) = 1 k! K CBD- n. (k-1)!(n-K)! (H) t.nl K Right side n (A1) = () – (*1)! (*)! XD) ? (_*) ] Left side = Right Side { n(n-)=n! therfore proved

Algebric proof K(X) = *Q) = kn! K! (n-k)!. R.H.S is. n (1) (n-1)! In (K-1)! (n-1 - (x-1)! n. (nl)! (K-1)! (-x)! kn (0-1)! Ko K-1)! (n-k?! 1 ni= n.) n!= n(n)! K. NI K. (k-1)! (n-W! K.nl KI (n-K)! K(2) Hop