Question

Given the sets: A = {x ∣ x < - 6} and B = {x ∣ x² < 18}, what is the expression for the interval? a) A = (- [infinity], - 6), B = (-√18, √18)

b) A = (- [infinity], - 6), B = (-√18, 6)
c) A = (- [infinity], - 6), B = (-√18, [infinity])
d) A = (- 6, - [infinity]), B = (-√18, [infinity])

Answer 1

The correct expression for the intervals of sets A and B is 'a) A = (-∞, -6), B = (-√18, √18)', with set A including all numbers less than -6 and set B including all numbers whose square is less than 18.

Step-by-step explanation:

To determine the correct expression for the intervals of the sets A and B, let's analyze each set based on the given definitions:

• Set A is defined as {x ∣ x < -6}, which means all numbers less than -6. Hence, the interval notation for set A is (-∞, -6).
• Set B is defined as {x ∣ x² < 18}. We need to find all the x values whose square is less than 18. By taking the square root of both sides, we get √18, which simplifies to approximately 4.24. Thus, x can be any number between -4.24 and 4.24, making the interval notation for set B (-√18, √18).

Using the correct interval notation, we can conclude that the correct expression for the intervals is:

• A = (-∞, -6)
• B = (-√18, √18)

Therefore, the answer is a) A = (-∞, -6), B = (-√18, √18).