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. (a) (3 points) 3 a triangle x s.t. White(x) True False Justify: (b) (3 points) squares x, Gray(x) A Below(z, d) O True False Justify: Gray() + Leftof(x,g) (c) (4 points) V circles I, O True False Justify: 2. Let P be the set of all people. Consider the following predicates, all with domain P: B(x) ="x lives in Boston" N(x) ="x lives in New York" D(x) ="x dances well" S(x) ="x is a good singer" 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 dances well (b) (3 points) "Every person either dances well or is a good singer" (e) (4 points) "Everyone who lives in New York does not live in Boston" a b A C d e 9 h i j k