Consider the predicate (relation) names I, M, K with arities 1, 2, 2, respectively, and a universe in which these predicates have the following meaning

I(u) : u was mentally impaired M(u,v) : u had a motive to kill v K(u,v) : u killed v.

Consider also the following statements. 1 : Someone killed Bert. 2 : Nobody was mentally impaired. 3 : If someone, not mentally impaired, killed Bert then this someone had a motive to kill him. 4 : Someone had a motive to kill Bert.

5 : Every mentally impaired killer has a motive to commit both, another murder and a suicide. Use the equality predicate == and the above predicates with the given meaning (but no other

predicates) to translate the five statements into Predicate Logic formulas 1, . . . , 5.