Question

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

Answer 1

Answer:

Option e is true

Step-by-step explanation:

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

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.$c\geq x$ for x belongs to A.

2.For all real number,if k is an upper bound  for A then,$k\geq c$

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.$c\leq x$ for x belongs to A.

2.For all real number,if k is lower  bound  for A then,$k\leq c$

Least upper bound=2

Greatest lower bound=1

Answer 2

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

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