Question

Given the sets A and B in interval notation A=(-[infinity], -6) ∪ (-6, [infinity]) and B=(-[infinity], -7) ∪ (-7, [infinity]), find A ∩ B.

a) (-[infinity], -6) ∪ (-7, [infinity])
b) (-[infinity], -6)
c) (-7, -6) ∪ (-6, [infinity])
d) (-7, [infinity])

Answer 1

The intersection of sets A and B is (-∞, -6) ∪ (-6, ∞).

Step-by-step explanation:

The intersection of sets A and B, denoted as A ∩ B, contains all the elements that are present in both sets A and B. To find this intersection, we need to identify the overlapping region between the intervals represented by A and B. In this case, A=(-∞, -6) ∪ (-6, ∞) and B=(-∞, -7) ∪ (-7, ∞).

First, let's determine the common range of the lower bounds of the intervals, which is the maximum of the two lower bounds. In this case, the lower bound of A is -∞ and the lower bound of B is -∞, so the common lower bound is -∞.

Now, let's determine the common range of the upper bounds of the intervals, which is the minimum of the two upper bounds. In this case, the upper bound of A is ∞ and the upper bound of B is ∞, so the common upper bound is ∞.

Putting it all together, the intersection of A and B is (-∞, -6) ∪ (-6, ∞). Therefore, the correct answer is option a) (-∞, -6) ∪ (-7, ∞).