Translate each of the following English statements into logical expressions. The domain is the set of all real numbers. (a) There are two numbers whose ratio is less than 1. (b) The reciprocal of every positive number is also positive. (c) There are two numbers whose sum is equal to their product. (d) The ratio of every two positive numbers is also positive.

Step-by-step explanations:

Since the domain is a set of all real numbers, all the expression are with respect to real numbers.

a. 3 x,y : x/y < 1 ∧ y/x < 1

b. ∀x > 0, 1/x > 0

c. 3 x,y : x + y = xy

d. ∀x > 0 ∧ y > 0, x/y > 0 ∧ y/x > 0.

3 means "there exists"

∀ means "for every value of"

∧ means "and"

answer: on kudzu, being female and being green are independent events.

step-by-step explanation: