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An affine (respectively projective) failed design \(D\), denoted by \(\text{AFD}(q)\) (respectively \(\text{PFD}(q)\)) is a configuration of \(v = q^2\) points, \(b = q^2 + q + 1\) blocks and block size \(k = q\) (respectively \(v = q^2 + q + 1\) points, \(b = q^2 + q + 2\) blocks and block size \(k = q + 1\)) such that every pair of points occurs in at least one block of \(D\) and \(D\) is minimal, that is, \(D\) has no block whose deletion gives an affine plane (respectively a projective plane) of order \(q\). These configurations were studied by Mendelsohn and Assaf and they conjectured that an \(\text{AFD}(q)\) exists if an affine plane of order \(q\) exists and a \(\text{PFD}(q)\) never exists. In this paper, it is shown that an \(\text{AFD}(5)\) does not exist and, therefore, the first conjecture is false in general, \(\text{AFD}(q^2)\) exists if \(q\) is a prime power and the second conjecture is true, that is, \(\text{PFD}(q)\) never exists.