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

Option e is true

Step-by-step explanation:

Set:{x/x}

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. for x belongs to A.

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

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. for x belongs to A.

2.For all real number,if k is lower  bound  for A then,

Least upper bound=2

Greatest lower bound=1

idk

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is