1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
lesantik [10]
3 years ago
6

Let A, B R be non-empty sets. Suppose that A B. Suppose that B has a least upper bound. Prove that A has a least upper bound, an

d lub A lessthanorequalto lub B.
Mathematics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer with explanation:

Given → A, B ⊆R, are non-empty sets.

Also, A ⊆ B.

It is also given that , B has least upper bound.

To Prove:→A has a least upper bound,

and → lub A ≤ lub B.

Proof:

    A and B are non empty sets.

Also, A ⊆ B

it means there are some elements in B which is not in A and there are some elements in set B which may be greater or smaller than or equal to set A.

The meaning of least upper bound is the the smallest member of the set from which all members are greater.

As, A⊆B

So, there are two possibilities ,either

→ Least upper bound set A = least upper bound set B------(1)

→ Least upper bound set A < least upper bound set B-------(2)

Combining (1) and (2)

→→→l u b(A) ≤ l u b (B)

   

 

You might be interested in
Worth a lot of points
lara [203]

Answer: -2, 2

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Which is larger 2/3" x 3-7/16" or 0.6"L x 3.43"W?
Darina [25.2K]
2/3 x (3 - 7/16) = (2/3) * (3+7/16)
       = (2/3)*(55/16)
       = 55/24
       = 2.2917

0.6 x 3.43
      = 2.058

The first answer is greater than the second.

Answer:  2/3 x 3-7/16 is larger.

5 0
3 years ago
A is directly proportional to the cube of B<br>When A=54, B=3<br>Find A when b=4​
vesna_86 [32]

Answer:

a=72

Step-by-step explanation:

54/3=18

18*4=72

a=72 when b=4

5 0
3 years ago
Which store offers the lowest unit rate for lettuce in dollars per pound?
vlabodo [156]
Answer: Farm Fresh

Explanation: Farm Fresh offers the lowest unit rate for lettuce, in dollars per pound. It after the lettuce at a lower price compared to the rest
5 0
3 years ago
A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4
Romashka-Z-Leto [24]

Answer:

You have to find the probability of all the numbers out of 6

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Thirty coins,all dimes and nickels,are worth $2.60. How many nickels are there?
    15·1 answer
  • Melanie buys a carrying case for her new laptop computer. The retail price is $24.50 and the sales tax is 7%. What is the amount
    11·1 answer
  • -13 times the difference between a number and 60 is equal to the number plus -59
    9·1 answer
  • The asset turnover of Ryan Company is 7.2. The total assets of Ryan are $88,000. Ryan's net sales were:
    12·1 answer
  • A group of individuals were surveyed about their plans for vacation. There were 21 individuals who said they were going to the d
    6·1 answer
  • Find the value of x.
    15·1 answer
  • A bingo card has 25 spaces but 1 free space, and if the card deck is 100 cards how do i know how many game cards i need for play
    6·1 answer
  • Find the equation of the graphed line, please select the best answer from the choices provided.​
    15·1 answer
  • What is the range of the data set?
    9·1 answer
  • As Sales Manager for ISeeYou Productions, you are planning to review the prices you charge clients for television advertisement
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!