Let A = {1,2,3), B = {a,b,c), and C= {x.x.z}. Consider the following relations R and...

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Let A = {1,2,3), B = {a,b,c), and C= {x.x.z}. Consider the following relations R and S from A to B and from B to C, respectively. R = {(1,b), (2, a),(2,c)} and S = {(a,x),(b.x),(c.x),(cz)} (a) Find thecomposition relation R-S. (b) Find the matrices MR,MS, and MR-S of the respective relations R, S, and R-S, and compare MR-S to the product MR MS. (c) Draw the arrow diagram of the relations R and S as in Fig. 2-7(a). Observe that 1 in A is "connected" to x in C by the path 1 bx; hence (1, x) belongs to R-S. Similarly, (2, y) and (2, z) belong to R-S. Let A = {1,2,3), B = {a,b,c), and C= {x.x.z}. Consider the following relations R and S from A to B and from B to C, respectively. R = {(1,b), (2, a),(2,c)} and S = {(a,x),(b.x),(c.x),(cz)} (a) Find thecomposition relation R-S. (b) Find the matrices MR,MS, and MR-S of the respective relations R, S, and R-S, and compare MR-S to the product MR MS. (c) Draw the arrow diagram of the relations R and S as in Fig. 2-7(a). Observe that 1 in A is "connected" to x in C by the path 1 bx; hence (1, x) belongs to R-S. Similarly, (2, y) and (2, z) belong to R-S.

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