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1 1 1 1 0 1 m r 0 1 1 m s 0 1 0 0 0 1 1 0 1 a if we

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A = {a,b,c} represented by the matrices given below. 1 1 1 1 0 1 M R = 0 1 1 M S = 0 1 0 0 0 1 1 0 1 (a) If we assume that the matrices were constructed using the order listed above for the set A, then S = (b) What is the matrix representing R S? M R S = (c) Construct the matrix representing the relation T = R -1 that is the inverse of R. M T = _________________________________________________________________ 4. (10 pts.) (a) What is the numerical value of the postfix expression below? 3 2 * 2 5 3 - 8 4 / * - = (b) What is the numerical value of the prefix expression below? + - * 2 3 5 / 2 3 4 =
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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. 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 . (b) Now draw the underlying undirected graph G 2 for the directed graph G 1 of part (a) of this problem. (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. _________________________________________________________________ 6. (10 pts.) Recall that the composition of two relations R and S on a set A is given by S R = { (a,c) ε A × A ( b)(b ε A and (a,b) ε R and (b,c) ε S)}.
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