Determine the intersection X ∩ Y. Express the answer in interval notation.X = {x | x ≥≥18} and Y= {x | x < 11}Select one:a. (11, 18]b. { }c. (-∞, 11] U (18, ∞)d. [11, 18)
Question
Determine the intersection X ∩ Y. Express the answer in interval notation.X = {x | x ≥≥18} and Y= {x | x < 11}Select one:a. (11, 18]b. { }c. (-∞, 11] U (18, ∞)d. [11, 18)
Solution
The intersection of X and Y, denoted as X ∩ Y, represents the set of elements that are common to both X and Y.
Given X = {x | x ≥ 18} and Y = {x | x < 11}, we can see that there are no common elements between X and Y.
The set X includes all numbers that are greater than or equal to 18, while the set Y includes all numbers that are less than 11. There is no number that can be both greater than or equal to 18 and less than 11 at the same time.
Therefore, the intersection of X and Y is an empty set, which is represented as { } in set notation.
So, the correct answer is b. { }
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