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Find the intersection and union of sets as indicated. Write the answers in interval notation. Express numbers as decimals.

a. (−3.5,1.4)∩(−2.7,4.9)
b. (−3.5,1.4)∪(−2.7,4.9)

(A) [−3.5,1.4] and [−3.5,4.9]
(B) [−2.7,1.4] and [−3.5,4.9]
(C) (−2.7,1.4) and [−3.5,4.9]
(D) (−2.7,1.4) and [−2.7,4.9]

1 Answer

4 votes

Final answer:

The intersection of the intervals (−3.5,1.4) and (−2.7,4.9) is (−2.7,1.4), and their union is (−3.5,4.9). The correct option is (C) (−2.7,1.4) and [−3.5,4.9].

Step-by-step explanation:

To find the intersection of the intervals (−3.5,1.4) and (−2.7,4.9), we look for the range of numbers that are in both intervals. The intersection begins at the higher of the two starting points and ends at the lower of the two endpoints, resulting in the interval (−2.7, 1.4). For the union of (−3.5,1.4) and (−2.7,4.9), we combine the ranges covered by both intervals. This starts at the lowest beginning number and ends at the highest endpoint of the two intervals, giving us the interval (−3.5,4.9). Based on the given intervals and the operations performed, the correct answers are Intersection: (−2.7,1.4), Union: (−3.5,4.9). Therefore, the correct option is (C) (−2.7,1.4) and [−3.5,4.9].

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