Consider the following zero-one matrix 1110 1110 0 0 01 18. ldentify the correct

Question

Consider the following zero-one matrix 1110 1110 0 0 01 18. ldentify the correct statement about the transitive property of the relation represented by the given matri. Since for every ordered pair (a, b) and (b, c,the ordered pair (a, cy is present in the relation, the relation is trensitive. O since for every ordered pair (a, b) and (b, c),the ordered pair (a, c) is present in the relation, the relation is transitive Since for every ordered pair (8, b) and (b. c)the ordered pair (a c) is not present in the relation, the relation is not transitive O Since for every ordered pair (a·b) and (b, c)the ordered pair (a, o) is not present in the relation, the relation is not transitive

Explanation / Answer

The given matrix is an equivalence relation, since it is reflexive (all diagonal elements are 1's, it is symmetric as well as transitive.

18. Since for every ordered pair (a,b) and (b,c) the ordered pair (a,c) is present in the relation, the relation is transitive

19. Since for every ordered pair (a,b), the ordered pair (b,a) is present in the relation, the relation is symmetric.

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