Let n be a positive integer and let X = {1,2,...,n}. Suppose that Ris a symmetric and transitive relation on X satisfying the following condition: In the matrix of the relation R (relative to the ordering 1,2,...,n), every row has at least one nonzero entry. Order 7 of the following sentences so that they form a proof for the following statment: Ris an equivalence relation on X. Your Proof: Choose from these sentences: Since R is symmetric and transitive, in order to show that Ris an equivalence relation, we only need to show that it is reflexive. Therefore R is reflexive. Since (x,y),(y,x) R and R is transitive, we have (3,2) E R. Since (x, y) R and R is symmetric, we have (3,1) E R. Since the matrix of relation R has a nonzero entry in the row corresponding to x, there is at least one element y e X such that (x,y) R. Suppose (x,y),(y, a) ER For an arbitrary X, we have shown that (2, 1) ER Since R is symmetric and transitive, in order to show that is an equivalence relation, we must show that it is reflexive and not antisymmetric. Therefore R is not antisymmetric. Suppose : Ex