. Question 2 Let P(I, y) be the predicate " has greeted y". The domain consists of all kids in the room. Use quantifiers to express the statement "Every kid in the room has been greeted by at least one kid in the room." in symbolic form. OFy, Vr, P(I, y) (f'D)d'RA'TAO O 1r, ly, P(I, y) (f 'D)d'IE'SAO Or, Vy, P(I, y) (1'I) d'RE'TAO Now let Q(I, y) be the predicate "I has won ?". The domain for I consists of all teams in the league and for y consists of all games this season. Use quantifiers to express the statement "There is some team in the league that has won every game this season."in symbolic form. O Ty, Vr, P(I, y) (6') d'RE'TAO O 1x, ly, P(I, y) OFr, Vy, P(I, y)Let P(z,y) be the predicate \"T has chased 3. The domain consists of all dogs in the park. Express the quantification Jy, z, P(x,y) as an English sentence. ) Every dog in the park has chased every dog in the park. Every dog in the park has been chased by at least one dog in the park. 0 There is some dog in the park that has chased some dog in the park. 0 There is some dog in the park that has been chased by every dog in the park. ) Every dog in the park has chased at least one dog in the park. _ There is some dog in the park that has chased every dog in the park. Now let QNx,y) be the predicate "I has visited '. The domain for Z consists of all explarers in the waorld and for y consists of all locations on the map. Express the quantification 3z, Jy, P(x, ) as an Enslish sentence. ) Every location on the map has been visited by at least one explorer in the world. Every explorer in the world has visited at least one location on the map. ) There is some explorer in the world that has visited some location on the map. ) There is some explorer in the world that has visited every location on the map. ) Every explorer in the world has visited every location on the map. ) There is some location on the map that has been visited by every explorer in the world. Find a counterexample to the statement: T, vy, (y =3z 4) v (y > 4) sume the domain for both variables consists of all real numbers. Hint: Graph the inequalities and identify the corresponding region of the zy-plane. x