What is the meaning of "Then S ∖m [tex]\neq[/tex]∅; otherwise S is a subset of a finite set; a contradiction"?

$What Is The Meaning Of "Then S M [tex]\neq[/tex]; Otherwise S Is A Subset Of A Finite Set; A Contradiction"?$

Answers

Answer 1

The phrase "Then S ∖m ∅; otherwise S is a subset of a finite set; a contradiction" is expressing a logical statement and its implications. Let's break it down:

"S ∖m ∅" means that the set difference between S and m is not empty. In other words, there is at least one element in S that is not in m."Otherwise S is a subset of a finite set" suggests that if the set difference is empty, then S must be a subset of a finite set. This implies that S has a limited number of elements.A contradiction" indicates that the statements in points 1 and 2 cannot both be true simultaneously because they contradict each other. If S has at least one element not in m (point 1), it cannot be a subset of a finite set (point 2).In summary, the statement is asserting that if the set difference between S and m is not empty, it contradicts the notion that S is a subset of a finite set.

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Related Questions

NO LINKS!! URGENT HELP PLEASE!!!
11. Write the equation for the graph

Answers

Answer: [tex]\text{y} = \sqrt{4(\text{x}+5)}-1[/tex]

This is the same as writing y = sqrt(4(x+5)) - 1

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Explanation:

The given graph appears to be a square root function.

The marked points on the curve are:

(-4,1)(-1,3)(4,5)

Reflect those points over the line y = x. This will have us swap the x and y coordinates.

(-4,1) becomes (1,-4)(-1,3) becomes (3,-1)(4,5) becomes (5,4)

Recall the process of reflecting over y = x means we're looking at the inverse. The inverse of a square root function is a quadratic.

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Let's find the quadratic curve that passes through (1,-4), (3,-1) and (5,4).

Plug the coordinates of each point into the template y = ax^2+bx+c.

For instance, plug in x = 1 and y = -4 to get...

y = ax^2+bx+c

-4 = a*1^2+b*1+c

-4 = a+b+c

Do the same for (3,-1) and you should get the equation -1 = 9a+3b+c

Repeat for (5,4) and you should get 4 = 25a+5b+c

We have this system of equations

-4 = a+b+c-1 = 9a+3b+c4 = 25a+5b+c

Use substitution, elimination, or a matrix to solve that system. I'll skip steps, but you should get (a,b,c) = (1/4, 1/2, -19/4) as the solution to that system.

In other words

a = 1/4, b = 1/2, c = -19/4

We go from y = ax^2+bx+c to y = (1/4)x^2+(1/2)x-19/4

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Next we complete the square

y = (1/4)x^2+(1/2)x-19/4

y = (1/4)( x^2+2x )-19/4

y = (1/4)( x^2+2x+0 )-19/4

y = (1/4)( x^2+2x+1-1 )-19/4

y = (1/4)( (x^2+2x+1)-1 )-19/4

y = (1/4)( (x+1)^2-1 )-19/4

y = (1/4)(x+1)^2- 1/4 - 19/4

y = (1/4)(x+1)^2 + (-1-19)/4

y = (1/4)(x+1)^2 - 20/4

y = (1/4)(x+1)^2 - 5

The equation is in vertex form with (-1,-5) as the vertex. It's the lowest point on this parabola. Placing it into vertex form allows us to find the inverse fairly quickly.

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The last batch of steps is to find the inverse.

Swap x and y. Then solve for y.

y = (1/4)(x+1)^2 - 5

x = (1/4)(y+1)^2 - 5

x+5 = (1/4)(y+1)^2

(1/4)(y+1)^2 = x+5

(y+1)^2 = 4(x+5)

y+1 = sqrt(4(x+5))

y = sqrt(4(x+5)) - 1

I'll let the student check each point to confirm they are on the curve y = sqrt(4(x+5)) - 1.

You can also use a tool like GeoGebra to verify the answer.

What is the domain of this function?

Answers

Answer:

[0,∞)

Step-by-step explanation:

The domain is just all the x values in the function. We can see in the graph that it starts at x=0 (inclusive per the filled in circle) and keeps going to the right forever (per the arrow at the end of the line). Therefore, x values for this function go from 0 to ∞.

thus, the domain is [0,∞)

60, 69, 79, 80, 86, 86, 86, 89, 90, 100
Which test score is an outlier?

60
69
90
100

Answers

The test score that is an outlier is 60. Option A

What is an outlier

A data point that dramatically deviates from the dataset's main pattern or trend is referred to as an outlier.

From the information given, we have that;

The score are;

60, 69, 79, 80, 86, 86, 86, 89, 90, and 100.

We can see that the outlier is 60.

This is due to the fact that all of the other scores, which range from 69 to 100, are considerably higher and closer in value.

The score of 60, however, is considerably lower than the others pupils.

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if Ra radius is 10cm , what will be the diameter and the area of the circle

Answers

Answer:

Diameter=20 cm, Area=100[tex]\pi[/tex]

Step-by-step explanation:

To find the diamter of a circle (given the radius), you multiply the radius by 2. 10cm*2=20 cm. The area of a circle is the radius squared times pi. 10^2 times pi is equal to 100[tex]\pi[/tex].

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