A predicate is a sentence that contains a finite number of variables and becomes a statement when specific values are substituted for the variables. If P(x) is a predicate: Define: what is the domain for P? (give a definition, not an example - don't tell me "The Real Numbers"). Define: what is the truth set for P? (Both questions are short answer; one sentence each should do).

Consider the open statement P(t) which says (∃x)(tx = 20).  Find the full truth set for P if the universal set is R.

Construct a truth table

Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y

answer

Let P(x) be the predicate "-6 < x ≤ 6" and let domain D = set of all even integers.  What is the truth set T for ?∈?x∈D (in set-roster notation)?

Create a truth table according to these specifications: There are 3 input bits, x2, x1, x0, and 2 output bits, s1, s0. The 2-bit output is the largest number of consecutive I's in the 3 input bits. (x2 is the most significant bit of the input, and s1 is the most significant bit of the output.) For example, input 000 gives output 00 (no 1’s), inputs 001 and 010 give output 01, input 011 gives output 10, etc. Show all 8 rows of the table clearly.

Determine the truth value of the statement: if the domain of the variables consists of the positive (non-zero), real number ∃a∀b(b4 >a)

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)