Let R be the relation represented by the matrix MR1 1 0 Find the matrix representing...
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.
Is the relation represented by the following matrix an
equivalence relation? Is it a partial order? Explain why or why
not.
find R foreach of the following by tracing and then Warshall 1. Find the adjacency matrix and adjacency relation for the following graph 2. Find the adjacency matrix and adjacency relation for the following graph 3. Find the corresponding directed graph and adjacency relation for the following adjacency matrix. TO 0 A = 0 0 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 1 0] 1 0 0 0
Please explain in detail!!
4. If binary relation R is given by matrix [1 0 1 0 1 101 м, 1 1 1 0 1 1 0 1 determine, if R is: (a) reflexive (b) symmetric (c) antisymmetric (d) transitive?
detail steps please
1· Let L:R'→R' bedefined by L(x,y)-(x-2y,x+2y Let S- (1.-1).(0.D)be a basis for R' and let T be the natural basis for IR2 Find the matrix representing L w. r to a) S b) Sand T c T andS d) T e) Compute L(2,-1) using the definition of L and also using the matrices obtained in a), b), c)and d)
Can someone please help me?
12. Let A = {1,2,3,4,5,6} and R be the relation on A whose matrix is [1 0 0 1 1 1 0 1 1 0 0 0 0 1 1 0 0 0 MR= 1 0 0 1 1 1 1 0 0 1 1 1 1 0 0 1 1 1 (a) Use MR to explain why R is an equivalence relation. (b) Compute A/R. (c) Draw the directed graph of (A, R).
3. [5 marks] Use the connectivity relation Mi= MRVM V... V Mehr to find the transitive closure of the relation R represented by the zero-one matrix 1 0 1 0 1 1 1 0 0 MR
4. Let TB:R" + R" and TA: RM → RP be the linear transformations represented by an mxn matrix B = [bj] and p x m matrix A = [ai;], that is, b11x1 + ... binin y = TB(x): bm121 + ... + bmnan 01191 +... 01mYm 21 :| = z=TA(y) : apıyı + ... + Apmym where x= y= 53 z= : represent vectors in R", RM, RP, respectively. Then, we know from Problem 3 that the com- position...
Let the relation R be defined on the set {x ∈ R | 0 ≤ x ≤ 1} by xRy ⇔ ∃t(x + t = y and 0 ≤ t ≤ 1) Is R transitive?
Please answer all!!
17. (a) Let R be the relation on Z be defined by a R b if a² + 1 = 62 + 1 for a, b e Z. Show that R is an equivalence relation. (b) Find these equivalence classes: [0], [2], and [7]. 8. Let A, B, C and D be sets. Prove that (A x B) U (C x D) C (AUC) Ⓡ (BUD).