Variable Domain and Statements

Which statement is true for the domain of the variable x being set of all integers?

a. There exists x (3x = 1)

b. There exists x (x squared less than 1)

c. For all x (x squared equals 1)

d. There exists x (x squared less than 0)

Answer:

The statement that is true for the domain of the variable x being set of all integers is: a. There exists x (3x = 1).

The domain for variable x is the set of all integers, which means x can take on any integer value whether positive, negative, or zero. In this case, we need to choose the statement that holds true for any integer value of x.

The statement "There exists x (3x = 1)" is true as it can be solved by replacing x with 1/3, which is a rational number. This statement holds true for any integer value of x, making it the correct choice.

It is important to understand the domain of variables when dealing with mathematical statements and equations. By knowing the possible values that a variable can take, we can determine the validity of different statements and solutions.