A relation p on the set X = {a,b,c,d} is represented by the following Boolean matrix.1 0 1 11 1 0 10 1 1 01 1 0 0Which of the properties below does p have? A It is reflexive. B It is symmetric. C It is transitive. D It is an equivalence relation. E None of the above.

To determine the properties of the relation p, we need to analyze the given Boolean matrix.

A. Reflexive: A relation is reflexive if every element is related to itself. In terms of the matrix, this means that all the diagonal elements (from top left to bottom right) should be 1. Looking at the matrix, we see that this is the case. So, the relation is reflexive.

B. Symmetric: A relation is symmetric if for every pair (a, b), if a is related to b then b is also related to a. In terms of the matrix, this means that the matrix should be the same when flipped over its diagonal. Looking at the matrix, we see that this is not the case (for example, the second element in the first row is 0, but the first element in the second row is 1). So, the relation is not symmetric.

C. Transitive: A relation is transitive if for every pair (a, b) and (b, c), if a is related to b and b is related to c, then a is also related to c. This is a bit more complex to check in the matrix, but if we look carefully, we can see that this property is not satisfied (for example, a is related to b and b is related to c, but a is not related to c). So, the relation is not transitive.

D. Equivalence relation: A relation is an equivalence relation if it is reflexive, symmetric, and transitive. Since the relation is not symmetric and not transitive, it is not an equivalence relation.

E. None of the above: Since the relation is reflexive, this option is not correct.

So, the only property that the relation p has is that it is reflexive.