Determine the intersection X ∩ Y. Express the answer in interval notation.X = {x | x ≥ -2} and Y = {x | x < -6}Select one:a. (-6, -2]b. [-6, -2)c. { } d. (-∞, -6] (-2, ∞)
Question
Determine the intersection X ∩ Y. Express the answer in interval notation.X = {x | x ≥ -2} and Y = {x | x < -6}Select one:a. (-6, -2]b. [-6, -2)c. { } d. (-∞, -6] (-2, ∞)
Solution
c. { }
The intersection of X and Y is the set of elements that are common to both X and Y.
X = {x | x ≥ -2} includes all real numbers greater than or equal to -2.
Y = {x | x < -6} includes all real numbers less than -6.
There are no numbers that are both greater than or equal to -2 and less than -6. Therefore, the intersection of X and Y is the empty set, which is represented as { } in set notation.
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