A Truth Table as a Function Let p, q, and r be statements. Let S {T, F}. %3D a) Write the set that contains all of the possible truth values of the three statements S x S x S. Hint: The first ordered triple in a truth table would be written (T, T, T). Let S x S x S be the domain of f with codomain S = {T, F} ST ifq is T F ifq is F Define f(p, q, r) = { %3D b) Write f as a set of ordered pairs. Hint: The ordered pair for an input of (T, T, T) and an output of T would be ((T, T,T), T)

A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refers to whether person x is an officer of the club. The predicate D(x) indicates whether person x has paid his or her club dues. The domain is the set of all members of the club. The names of the members and their truth values for each of the predicates is given in the following table. Indicate whether each expression is true or false. If a universal statement is not true, give a counterexample. If an existential statement is true, give an example. Name M(x) O(x) D(X) Hillary T F Bernie F F Donald F F Jeb F Carly F F Ex (M(x) A D(x)

Predicate Logic answer a & b

Construct a truth table for the statement p<(pvq). Complete the truth table. q pvq -p+(pvq) T T ▼ T F F T F LL LL

Suppose the domain of the propositional function p(x) consists of the integers -2, -1, 0, 1, and 2. Write the following proposition using disjunctions, conjunctions, and negations. Vx-p(x)