Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 1 0 1 07 Consider the following zero-one matrix 0 1 0 1 1 0 1 0 0 1 0 1] representing a relation on the ordered set (a, b, c, d).
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- O Give the matrix representation for the relation depicted in the arrow dia- gram. Then, express the relation as a set of ordered pairs. The arrow diagram below represents a relation. 2PLEASE TYPE ONLY IF NOT TYPE THAN DO NOT DO IT**** Exercise 8.1.1: Matrices to arrow diagrams and sets.Each matrix below represents a relation. The rows and columns are numbered 1 through 3 or 4. Give the arrow diagram for each matrix, then express each relation as a set of ordered pairs.Consider the relation on A = {a, b, c, d, e} given by R = {(a,b), (b,c),(b,d), (b,e),(d,e)}
- LO 5 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 1 1 1 0 1 1 representing a relation on the ordered set (a, b, c). 1 1 1 Consider the following zero-one matrix Identify the true statement about the symmetric property of the relation in the given matrix. (You must provide an answer before moving to the next part.) Multiple Choice The (1, 2)th element is not equal to the (2, 1)th element. So, the relation is not symmetric. The (1, 2)th element is not equal to the (2, 1)th element. So, the relation is symmetric. The (1, 2)th element is equal to the (2, 1)th element. So, the relation is not symmetric. The relation is symmetric because all the diagonal elements are Os.40 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 1 1 1 representing a relation on the ordered set (a, b, c). Consider the following zero-one matrix 01 1 1 1 The relation in the given matrix is not an equivalence relation. True or False True FalseLet P={{a,b,d},{c,f},{e,g}} be a partition. Write the relation matrix for the implied equivalence relation.
- 101 Let R be the relation represented by the matrix MR and S be the relation represented by the matrix M= Then the Matrix representing RNS is given by O O O O O OQuestion Number 05 | Page 2 of 4 a) For the relation R on the set {1, 2, 3, 4}, decide whether it is reflexive, whether it is an equivalence relation. R = {(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)} b) Determine whether the relation represented by the zero-one matrix is a poset (partial order set): [1 1 1 1 Lo 1 1.4 4 Let A = 2 3 1 and b = -1 -5 -6 -5 Yes 1. Determine if b is a linear combination of a1, a2 and a3, the columns of the matrix A. If it is a linear combination, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, enter O's for the coefficients. ai+ a2+ az = b.
- 28 Required information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 1 1 1 0 1110 1 1 1 0 0001 Consider the following zero-one matrix The relation represented by the given matrix is not an equivalence relation. True or False True representing a relation on the ordered set (a, b, c, d). FalseRequired information NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. 1 1 1 07 Consider the following zero-one matrix True or False The relation represented by the given matrix is not an equivalence relation. True 10 1 1 10 0 0 0 1 False representing a relation on the ordered set (a, b, c, d).Write distinct if the activity/situation illustrates a permutation of distinct objects and write not if it does not.