Question

Use set builder notation to express the set of all positive even integers strictly greater than 100. Select the correct answer below:

a. (2x|x € Z and x > 100)
b. {2x|x € R and x < 50)
c. 2x
d. x€ Z and x > 100

Answer 1

The correct set builder notation for all positive even integers strictly greater than 100 is x ∈ Z and x > 50, where '2x' represents the even numbers and 'x > 50' ensures these numbers are greater than 100 when multiplied by 2.

Step-by-step explanation:

The set of all positive even integers strictly greater than 100 can be expressed in set builder notation as follows:

x ∈ Z and x > 50

In set builder notation, the description of the set consists of two parts: a variable that represents the elements of the set and a condition that must be satisfied for an integer to be included in the set. In this case, '2x' represents the even integers, 'x ∈ Z' indicates that x is an integer, and 'x>50' ensures that the even numbers are strictly greater than 100 when multiplied by 2. Therefore, the correct answer is option c.