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# M r s m r m r c construct the matrix representing the

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M R S = M R M R = (c) Construct the matrix representing the relationT=R -1 that is the inverse of R. 100 M T = M R T = 110 _________________________________________________________________ 4. (10 pts.) (a) What is the numerical value of the postfix expression below? 32*2 53-84/*- = 62 = 3 653-84/*- = 3 6284/*- = 3 622*- = 3 64- =3 2 (b) What is the numerical value of the prefix expression below? +-*235/ 234 = +-*235/84 = +-*2352 = +-652 = +12

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TEST3/MAD2104 Page 3 of 4 _________________________________________________________________ 5. (15 pts.) (a) Draw a directed graph G 1 whose adjacency matrix is given on the left below.// V 1 ={a ,b ,c ,d} . 0100 0011 0001 0000 . (b) Now draw the underlying undirected graph G 2 for the directed graph G 1 of part (a) of this problem.// V 2 . (c) Is G 2 =( V 2 ,E 2 ), above, isomorphic to the simple graph G 3 V 3 ,E 3 ) given below? Either display an isomorphism f:V 2 V 3 or very briefly explain why there is no such function by revealing an invariant that one graph has that the other doesn’t. Yes, define f:V 2 V 3 by f(a) = b, f(b) = c, f(c) = a, and f(d) = d. Then {a, b} ε E 2 { f(a), f(b)}={b ,c} ε E 3 , {b, c} ε E 2 { f(b), f(c)}={c ,a} ε E 3 , d} ε E 2 { f(b), f(d)}={c ε E 3 , {c, ε E 2 { f(c), f(d)}={a ε E 3 . [You could also use f(a) = b, f(b) = c, f(c) = d, and f(d) = a.] _________________________________________________________________ 6. (10 pts.) Recall that the composition of two relations R and S on a set A is given by SR={ (a,c) ε A×A ( b)(b ε A and (a,b) ε R and (b,c) ε S)}. Also, recall that the n th composition power of a relation on a set is defined recursively by R 1 = R, and for each n ε ,i f n 1, then R n+1 =R n R.
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M R S M R M R c Construct the matrix representing the...

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