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
PLEASE HELP i will give you a brainly
Lady bird [3.3K]

Answer:JKL and ∠RST are complementary.

m∠JKL = 36° and m∠RST = ( x + 15)°.

Find the value of x and the measure of ∠RST .

complementary angles are two angles whose sum is 90°

36%2Bx+%2B+15=90°

51%2Bx+=90°

x+=90-51°

x+=39°

->the measure of ∠RST== ( 39 + 15)=54°

both answer and explanation

8 0
3 years ago
Consider the graph and equation, y = 3x, that represent Alonso’s walking speed. What relationship is represented by this equatio
natita [175]

Answer:

The equation, y=3 x,

Step-by-step explanation:

y=Distance traveled

x =Total time

Also, in terms of straight line

Slope =3= uniform Velocity

Point (3,9) and (5,15) represents Distance traveled in 3 (unit of time) =9 unit, and 15 unit=Distance traveled in 5 (Unit of time).

→Alonso is moving with uniform speed=3 (unit of time), as velocity remains constant in the entire process.

6 0
3 years ago
Find the values of x and y.​
olchik [2.2K]

Answer:

value of x = 26

value of y = 26 \|2

( 26 root 2 )

Step-by-step explanation:

here's the solution : -

=》

\sin(45)  =   \frac{perpendicular}{hypotenuse}

=》

\frac{1}{ \sqrt{2} }  =  \frac{26}{y}

=》

y = 26 \sqrt{2}

and

\tan(45)  =  \frac{perpendicular}{base}

=》

1 =  \frac{26}{x}

=》

x = 26

8 0
3 years ago
Batteries produced by a manufacturing company have had a life expectancy of 135 hours. Because of an improved production process
Nikolay [14]

Answer:  c. z = 1.35; Reject the null hypothesis

Step-by-step explanation:

Let \mu be the average life expectancy of its batteries.

As per given , we have

Null hypothesis : H_0 : \mu =135

Alternative hypothesis : H_a : \mu >135

Since H_a is right-tailed and population standard deviation is also known, so we perform right-tailed z-test.

Test statistic : \dfrac{\overlien{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

where, n= sample size

\overlien{x}= sample mean

\mu= Population mean

\sigma=population standard deviation

For n=42,\ \overline{x}=140\ \&\ \sigma=24, we have

z=\dfrac{140-135}{\dfrac{24}{\sqrt{42}}}=1.35015431217\approx1.35

Critical one-tailed test value for 0.10 significance level :

z_{0.1}=1.28

 Decision : Since critical z value (1.28) < test statistic (1.35), so we reject the null hypothesis .

[When critical value is less than the test statistic value , we reject the null hypothesis .]

5 0
2 years ago
Drag a vertex of the triangle to change its shape.
likoan [24]

Answer:

The correct option is;

45°

Step-by-step explanation:

By angle sum theorem, we have that the sum of angles in a triangle = 180°

Therefore, we have;

When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;

The third angle + 60° + 75° = 180°

Which gives;

The third angle  = 180°- 60° - 75° = 180°- 135° = 45°

The measurement of the third angle by the angle sum theorem will be 45°

The correct option is ∠third angle = 45°.

8 0
3 years ago
Other questions:
  • 25% of 200 is _________.
    8·2 answers
  • Distribute5x (3x + 7)
    13·1 answer
  • Given the three side lengths, how can you tell if a triangle<br> is a right triangle?
    12·2 answers
  • Find the measure of the arc for abc
    8·1 answer
  • Which statement about the data is true? 985, 2, 18, 11, 512, 2, 14, 19, 112, 15
    13·1 answer
  • According to your model, what price should you charge to maximize profit? Explain how you know this is the best price. (Hint: Re
    14·1 answer
  • A basketball player scored 288 points in 9 games. Use the unit rate to find how many points the player would score in 5 games.
    13·1 answer
  • Are the following triangles similar by the angle-angle similarity theorem?
    10·2 answers
  • What would the equation be??​
    15·1 answer
  • This is more IXL i just nee d enough right answers and I'll be good to go.
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!