Question

Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the set: {x∣x∈[4,8]}

a) lub does not exist; glb =8
b) lub=4;glb=8
c) lub=8;glb=4
d) lub=4; glb does not exist
e) lub and glb do not exist

Answer 1

The least upper bound (lub) for the set x∈[4,8] is 8, and the greatest lower bound (glb) is 4, as they are the maximum and minimum values within the closed interval respectively. Therefore, the correct answer to the student's question is c) lub=8;glb=4.

Step-by-step explanation:

The student has asked to find the least upper bound (lub) and the greatest lower bound (glb) for the set: x∈[4,8]. The least upper bound is the smallest number that is greater than or equal to all elements of the set, while the greatest lower bound is the largest number that is less than or equal to all elements of the set. For the given set, the least upper bound is 8 since it is the highest number in the closed interval [4,8] and by definition, no number greater than 8 is within the set. Similarly, the greatest lower bound is 4 because it is the smallest number in the interval and no number less than 4 belongs to the set. Therefore, the correct answer to the student's question is c) lub=8;glb=4.