1. Investigate what are the following numbers and write the indicated sets:

(a) Natural numbers, denoted by N. Define a set of odd natural numbers.

(b) Integer numbers, denoted by Z. Define a set of integer numbers that are multiples of 3.

(c) Real numbers, denoted by R. Define a set of real numbers in the range of 5.545 and 9.854.

Given the predicate P(x) to be 7x + 3 is even.

(a) Find several values of n in which the predicate is true

(b) Use an existential quantifier to express a complete predicate

(c) Use a universal quantifier to express a complete predicate

2. Write the logical form of the following description: there is an odd number beween any two even numbers

3. Write the logical form of the following description: there is an even number beween any two odd numbers

4. Write the logical form of the following description: there is no number beween any two consecutive numbers

5. (a) Write the logical form of the following (informal) description: If P is in set A, then Q is in set B. If Q is not in set B, then P is in set A. Therefore, P is not in set A or Q is not in set B.

(b) Construct a truth table of the resulting logical expression.

6. Use a truth table to prove or disprove the following expression: (P (Q R)) = P (Q R)