Question

Use set builder notation to express the set of perfect squares between 1 and 1000 exclusively, i.e not including 1 and 1000.

Answer 1

The set of perfect squares between 1 and 1000 exclusively is represented in set builder notation as x = n², 1 < n² < 1000, n ∈ ℕ, which includes squares of integers from 2 to 31.

Step-by-step explanation:

The set of perfect squares between 1 and 1000 exclusively can be expressed in set builder notation as x = n², 1 < n² < 1000, n ∈ ℕ, where n represents any natural number. Perfect squares are numbers that can be expressed as the square of an integer. Since 1 and 1000 are excluded, we seek the squares of integers between 1 and the square root of 1000, which is approximately 31.6. Therefore, we consider squares of integers from 2 to 31, which are 4, 9, 16, ... , 961.