1. Let be a knowledge base in first-order logic in which axioms concerning kinship relations have been mapped. The objects of the knowledge base correspond to people, the knowledge base includes

the following predicates M(x,y) which is true only when person x is the mother of person y. AM (x,y) which is true only when individual x is a sibling of individual y from the same mother. • • The knowledge base also includes objects denoted as "HELEN", "JOHN", "COSTAS", "MARY" and denote the corresponding persons. Suppose the knowledge base includes the following logical propositions. M(HELEN,JOHN) M(HELEN, COSTAS) AM(MARY, COSTAS) Vx1,x2,x3 (M(x1,x2) M(x1,x3)) AM(x2,x3) n=> vy1,y2 AM(y1,y2)) AM (y2,y1)=> Vz1,z2,23 (AM(z1,z2) AM(z2, z3)) AM(z1,z3)n => vw1,w2,w3 (AM(w1,w2) M(w3,w2)) M(w3,w1)n=> A) Find the propositions resulting from the above knowledge base with the following substitutions: {x1/HELEN}, {X2/JOHN},{x3/COSTAS} {y1/JOHN},{y2/COSTAS} {z1/MARY}, {z2/COSTAS},{z3/JOHN} {w1/MARY}, {w2/COSTAS}, {w3/HELEN} B) To study if the above knowledge base covers the proposition AM(MARY, JOHN) M(HELEN, MARY). Please note that you should rely solely on the above knowledge base suggestions without using any other knowledge of kinship relationships.