3. [5 marks] Use the connectivity relation Mi= MRVM V... V Mehr to find the transitive...
4. [3 marks] Let R be a relation on a set A. Let A {1,2, 3, X, Y} and R = {(1, 1), (1,3), (2,1), (3, 1), (1, X), (X, Y)} (a) What is the reflexive closure of R? (b) What is the symmetric closure of R? (c) What is the transitive closure of R?
Use Warshall's Algorithm to find the transitive closure of the relation {(a,b), (b,a), (b,c), (b,e), (c,a), (d,c), (d,d), (e,c)} on {a, b, c, d, e}. Please leave your answer in matrix form.
please help box answer discrete math 4. Use Warshall's algorithm to find the transitive closure of the relation whose ordered pair representation is (01.3) (2.3),(2.4),(34) 4. Use Warshall's algorithm to find the transitive closure of the relation whose ordered pair representation is (01.3) (2.3),(2.4),(34)
8) Let R be a relation on the set A = {a, b, c} defined by R= {(a, a),(a, b), (a, c), (b, a), (b, b)}. (3 points)_a) Find Mr, the zero-one matrix representing R (with the elements of the set listed in alphabetical order). (2 points)_b) Is R reflexive? If not, give a counterexample. (2 points)_c) Find the symmetric closure of R. (3 points)_d) Find MR O MR.
3. (a) Let R be a binary relation on the set X = {1,2,3,4,5,6,7}, defined by R= {(1,3), (2,3), (3, 4), (4,4),(4,5), (5,6), (5,7)} (1) (6 pts) Find Rk for all k = 2, 3, 4, 5,... (2) (3 pts) Find the transitive closure t(R) of R by Washall's algorithm and draw the directed graph of t(R).
Question 3. Given the relation Ron A = {a,b,c,d,e) by the pairs R = {(a,b), (cb), (b, d), (e,d)} (a) (2 MARKS) Display the transitive closure R+ of R as a set of pairs. (b) (1 MARK) Explain why R+ is an order. Caution: An order has two defining properties. (c) (2 MARKS) Display the Hasse diagram of the order R+ (d) (1 MARK) Display the set of minimal members of R+.
Let R be the relation represented by the matrix MR1 1 0 Find the matrix representing R Го 2.
3. (a) If aRb is a relation of congruent modulo n, a ≡ b (mod n). Show that R is: (i) reflexive. (ii) symmetric. (iii) transitive. (b) A is a set and | A | = 8. R is a relation on A, R ⊆ A X A. (i) How many different R can be produced? (ii) How many R are reflexive? (iii) How many R are symmetric? (iv) How many R are reflexive and symmetric? (c) A computer application...
Question 5 [3+(2+4) marks] (a) The matrix A has a repeated eigenvalue of 1 = 2. During the solution of the solution (A-21)X = 0, the augmented matrix below appears. Find a basis for the eigenspace for this eigenvalue. Ti 0 -2 07 lo o o lo To ooo (b) (i) Show that if T(x) is a linear transformation from R" to R", that T(0) is the zero vector. (i) Assume that T(u) = 0 only when u = 0....
List the members of the equivalence relation on {1,2,3,4}. Find the equivalence classes [1],[2],[3],[4] for the followi {{1},{2},{3},{4}} Determine whether each relation is reflexive,antisymmetric , or transitive (x,y) in R if xy>1 (x,y) in R if x > y (x,y) in R if 3 divides x + 2y