Find the least upper bound (if it exists) and the greatest lower bound (if it exists) for the set: {x|x∈[1,2)} a) lub and glb do not exist b) lub = 1; glb does not exist c) lub does not exist; glb = 2 d) lub = 1; glb = 2 e) lub = 2; glb = 1

Respuesta :

Answer:

Option e is true

Step-by-step explanation:

Set:{x/x[tex]\in [1,2)[/tex]}

Least upper bound:

If a non empty set A and A has an upper bound.Then, the number c is least upper bound when it satisfied the following properties

1.[tex]c\geq x[/tex] for x belongs to A.

2.For all real number,if k is an upper bound  for A then,[tex]k\geq c[/tex]

Greatest lower bound:

If a non empty set A and A has lower bound.Then, the number c is greatest lower bound when it satisfied the following properties

1.[tex]c\leq x[/tex] for x belongs to A.

2.For all real number,if k is lower  bound  for A then,[tex]k\leq c[/tex]

Least upper bound=2

Greatest lower bound=1

The least upper bound and the greatest lower bound is (e) lub = 2; glb = 1

How to determine the bounds?

The set is given as:

{ x | x ∈ [1,2) }

The above means that the element x is an element of the set such that x is any value between 1 (inclusive) and 2 (exclusive)

The bound of the set means that;

The least upper bound and the greatest lower bound exist for the set.

The least upper bound is 2, while the greatest lower bound is 1

Hence, the true statement is (e) lub = 2; glb = 1

Read more about set bounds at:

https://brainly.com/question/24327896

ACCESS MORE
EDU ACCESS
Universidad de Mexico