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
Maurinko [17]
3 years ago
5

Let A be a set of numbers.

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
4 0

Answer:

a. closed under addition and multiplication

b. not closed under addition but closed under multiplication.

c. not closed under addition and multiplication

d. closed under addition and multiplication

e. not closed under addition but closed under multiplication

Step-by-step explanation:

a.

Let A be a set of all integers divisible by 5.

Let x,y∈A such that x=5m\,,\,y=5n

Find x+y,xy

x+y=5m+5n=5(m+n)

So, x+y is divisible by 5.

xy=(5m)(5n)=25mn=5(5mn)

So,

xy is divisible by 5.

Therefore, A is closed under addition and multiplication.

b.

Let  A = { 2n +1 | n ∈ Z}

Let x,y∈A such that x=2m+1\,,\,y=2n+1 where m, n ∈ Z.

Find x+y,xy

x+y=2m+1+2n+1=2m+2n+2=2(m+n+1)

So,

x+y ∉ A

xy=(2m+1)(2n+1)=4mn+2m+2n+1=2(2mn+m+n)+1

So,

xy∈ A

Therefore, A is not closed under addition but A is closed under multiplication.

c.

Let A=\{2,5,8,11,14,...\}

Let x=2,y=5 but x+y=2+5=7∉A

Also,

xy=2(5)=10∉A

Therefore, A is not closed under addition and multiplication.

d.

Let A = { 17n: n∈Z}

Let x,y ∈ A such that x=17n,y=17m

Find x + y and xy

x+y=17n+17m=17(n+m)

xy=(17m)(17n)=289mn=17(17mn)

So,

x+y,xy ∈ A

Therefore, A is closed under addition and multiplication.

e.

Let A be the set of nonzero real numbers.

Let x,y ∈ A such that x=-1,y=1

Find x + y

x+y=-1+1=0

So,

x+y ∈ A

Also, if x and y are two nonzero real numbers then xy is also a non-zero real number.

Therefore, A is not closed under addition but A is closed under multiplication.

You might be interested in
Which construction was completed in the diagram below?
KIM [24]

Answer:

A) angle bisector

Step-by-step explanation:

The ray drawn theough angle BOA creates 2 congruent angles.

5 0
2 years ago
there are 48 stickers in 2 sheets of stickers. which of the following expresses the ratio of stickers to sheets?
gregori [183]
2:48 is the answer for the question 
6 0
3 years ago
Which statement is true about the box plots? A number line goes from 0 to 13. Marc's class's whiskers range from 1 to 10, and th
klasskru [66]

here is the correct answer which is <u>D</u>

5 0
3 years ago
Read 2 more answers
Suppose a normal distribution has a mean of 222 and a standard deviation of 16. What is the probability that a data value is bet
valentina_108 [34]
Mean of the distribution = u = 222
Standard Deviation = s = 16

We have to find the probability that a value lies between 190 and 230.

First we need to convert these data values to z score.

z= \frac{x-u}{s}

For x = 190, 
z= \frac{190-222}{16}=-2

For x = 230
z= \frac{230-222}{16}=0.5

So, we have to find the percentage of values lying between z score of -2 and 0.5

P( -2 < z < 0.5) = P(0.5) - P(-2)

From standard z table, we can find and use these values.

P(-2 < x < 0.5 ) = 0.6915 - 0.0228 = 0.6687

Thus, there is 0.6887 probability that the data value will lie between 190 and 230 for the given distribution. 

5 0
3 years ago
Among other ingredients, a recipe for paella calls for 3/4 pound of chorizo and 1/2 cups of rice. What is the unit rate of pound
TEA [102]
The answer to the question is C.
4 0
3 years ago
Other questions:
  • Plz answer this question
    8·2 answers
  • 3 x 1/4 what is the answer to the question?
    7·2 answers
  • Write 29/10 in decimal form
    11·2 answers
  • There are 48 pounds of apples in a bushel. if apple pickers pick 320 pounds of apples, how many bushels are there and how many p
    5·1 answer
  • I just want people to tell me if this correct for the first question
    8·2 answers
  • What is the converse of the statement “If an angle is a right angle, then it measures 90 degrees”? ...?
    6·1 answer
  • Solve the equation 2/5x-1=9. Complete each step of the solution and check your solution
    13·1 answer
  • A car dealership owner created a data table to see how many new and used cars were sold over several months.
    11·2 answers
  • IS THIS CORRECT PLEASE
    5·2 answers
  • Finish the polynomial by adding one number to make it a perfect square<br><br> x^2+18x+
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!