Let S = {a, b, c). Find the following:a) the number of reflexive relations on Sb)the number of reflexive and symmetric relations on S

The number of reflexive relations on S  is 64.

The number of reflexive and symmetric relations on S  is 8.

Step-by-step explanation:

Consider the provided set S = {a, b, c}.

The number of elements in the provided set is 3.

Part (a) the number of reflexive relations on S

To calculate the number of reflexive relation on S we can use the formula as shown:

Total number of Reflexive Relations on a set:.

Where, n is the number of elements.

In the provided set we have 3 elements, so substitute the value of n in the above formula:

Hence, the number of reflexive relations on S  is 64.

Part(b) The number of reflexive and symmetric relations on S.

To calculate the number of reflexive and symmetric relation on S we can use the formula as shown:

Total number of Reflexive and symmetric Relations on a set:.

Where, n is the number of elements.

In the provided set we have 3 elements, so substitute the value of n in the above formula:

Hence, the number of reflexive and symmetric relations on S  is 8.

Related Questions

A restaurant has a capacity of 120 patrons. If the restaurant is full, how many patrons are at the restaurant?

Step-by-step explanation:

Find the​ range, variance, and standard deviation for the given sample data. Include appropriate units in the results.Listed below are the measured radiation absorption rates​ (in W/kg) corresponding to various cell phone models. If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?
0.950.95
0.730.73
0.630.63
0.910.91
1.321.32
1.481.48
0.630.63
1.231.23
0.910.91
1.411.41
0.670.67
The range of the sample data is
nothing

​(Round to three decimal places as​ needed.)
Sample standard
deviationequals=nothing

kg.kg.
left parenthesis Upper W divided by kg right parenthesis squared .W/kg2.
W.W.
Upper W divided by kg.W/kg.
​(Round to three decimal places as​ needed.)
Sample
varianceequals=nothing

kg.kg.
left parenthesis Upper W divided by kg right parenthesis squared .W/kg2.
Upper W divided by kg.W/kg.
W.W.
​(Round to three decimal places as​ needed.)
If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?
A. ​No, because it is necessary to have at least 5 of each cell phone in order to get a meaningful result. Only including one of each cell phone model is not representative of each cell phone model.
B. ​Yes, because the results from any sample of cell phones will be typical of the population.
C. ​Yes, because each model is being represented in the sample. Any sample that considers all possible cell phone models will produce results typical of the population of cell phones.
D. No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

D. No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Step-by-step explanation:

For this case we have the following data values:

0.95,0.73,0.63,0.91,1.32,1.48,0.63,1.23,0.91,1.41,0.67

The first step on this case is order the datase on increasing way and we got:

0.63 0.63 0.67 0.73 0.91 0.91 0.95 1.23 1.32 1.41 1.48

The range is defined as

And if we replace we got:

The sample standard deviation is given by this formula:

And if we replace we got

And the sample variance is just the standard deviation squared so we got:

And for the last question about : If one of each model is measured for radiation and the results are used to find the measures of​ variation, are the results typical of the population of cell phones that are in​ use?

We can conclude this:

D. No, because some models of cell phones will have a larger market share than others. Measures from different models should be weighted according to their size in the population.

Anyone got the answer to this? Ik it’s prob easy but I’m just not seeing it

y ≤0

Step-by-step explanation:

y =- x^2

x^2 is always positive or 0

Make this negative

- x^2 is negative or 0

The range is negative or 0

y ≤0

Step-by-step explanation:

y=-x^2

the range is(-∞,0]

y≤ 0 ( since the coefficient  a is negative it is open downward)

If tangent alpha equals negative StartFraction 21 Over 20 EndFraction ​, 90degreesless thanalphaless than180degrees​, then find the exact value of each of the following. a. sine StartFraction alpha Over 2 EndFraction b. cosine StartFraction alpha Over 2 EndFraction c. tangent StartFraction alpha Over 2 EndFraction

α= 133.6 degrees

(a)Sin(α/2)=0.9191

(b)cos(α/2)=0.3939

(c)Tan(α/2)=2.3332

Step-by-step explanation:

If Tan α=

90<α<180

We determine first the value of α in the first quadrant

α=

=46.4

Since 90<α<180

α=180-46.4=133.6 degrees

(a)Sin(α/2)=Sin(133.6/2)=Sin 66.8 =0.9191

(b)cos(α/2)=cos(133.6/2)=cos 66.8 =0.3939

(c)Tan(α/2)=Tan(133.6/2)=Tan 66.8 =2.3332

To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water. How do their two mixtures compare in taste?

Noah's mixture will taste more like orange, than Andre's mixture.

Step-by-step explanation:

Given:

Noah mixes 4 scoops of powder with 6 cups of water.

Means Noah ratio will be  or 0.67

Andre mixes 5 scoops of powder with 8 cups of water

Means Andre ratio will be  or 0.62

As,

or

0.66 > 0.62

We can say that content of orange powder will be more in Noah mixture than in Andre's Mixture.

Hence, Noah's mixture will taste more like orange, than Andre's mixture.

11 The net force on a vehicle that is accelerating at a rate of 1.5 m/s² is 2,800 newtons. What isthe mass of the vehicle to the nearest kilogram?

Step-by-step explanation:

Given

Required

Determine the mass of the vehicle

This question will be answered using Newton's second law

Substitute values for Force and Acceleration

Make Mass the subject

---- approximated

Hence, the mass of the vehicle is 1867kg