1. For each of the following statements, state whether it is true or false in the given Tarski's World (see next page). Justify each answer. Note: you must explain why the statement is true or false specifically in the given Tarski's World. Hint: (Leftof(x,y) V RightOf(x,y)) means that . and y are in the same column! (a) (3 points) 3 a triangle o s.t. V squares y, ~ (Leftof(x,y) V RightOf(x,y)) True False Justify: (b) (3 points) V squares y, 3 a triangle x s.t. ~ (Leftof(x,y) V RightOf(x,y)) True O Justify: (c) (4 points) V squares 1, V triangles y, SameColor(x, y) O True False Justify: 2. Let P be the set of all people. Consider the following predicates, all with domain P: A(x) ="x is an athlete" F(x) ="x runs fast" S(x,y) ="x is shorter than y" L(x, y) ="x likes y" Write the following statements formally, using the given predicates. The domain for all variables must be P; do not define new sets. There is no need to justify. (a) (3 points) "Someone is liked by everyone" (b) (3 points) "Someone is shorter than all athletes" (c) (4 points) "All athletes are shorter than all fast runners" b A. A e g h i j k