Question

Express each of these statements using predicates, quantifiers, logical connectives, and mathematical operators where the domain consists of all integers:

a. The average of two positive integers is positive.
b. The product of two negative integers is positive.
C. The difference of two negative integers is not necessarily negative.

Answer 1

The average of two positive integers is positive, the product of two negative integers is positive, and the difference of two negative integers is not necessarily negative.

Step-by-step explanation:

a. The average of two positive integers is positive can be expressed as:

∀x, y ∈ Z+ (x + y)/2 > 0

b. The product of two negative integers is positive can be expressed as:

∀x, y ∈ Z- xy > 0

c. The difference of two negative integers is not necessarily negative can be expressed as:

∃x, y ∈ Z- x - y ≥ 0