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2 years ago

Can you conclude that a = b if a and b are two sets with the same power set?

SAT

1 answer:

zalisa [80]2 years ago

4 0

The sets A and sets B contains items called elements

It is true that the set A is equal to set B

<h3>How to determine the true statement?</h3>

The sets are given as:

Set A and set B

Since the sets have the same power set, then we have:

P(A) = P(B)

The above means that:

For every element X in A, then the element is also in B

And

For every element Y not in A, then the element is also not in B

So, we can conclude that:

All subsets of the set A are subsets of the set B and vice versa

Hence, the set A is equal to set B

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Lydia graphed δlmn at the coordinates l (0, 0), m (2, 2), and n (2, −1). She thinks δlmn is a right triangle. Is lydia's asserti

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No product results in -1, hence δlmn is NOT a right triangle showing that lydia's assertion is incorrect

<h3>Perpendicular lines</h3>

In order to determine whether triangle lmn is right-angled, we need to determine the slope of lm, ln, and mn first as shown:

For the slope of lm:

$m_{lm} = \frac{2-0}{2-0}\\ m_{lm} =2/2\\m_{lm} =1$

For the slope of ln:

$m_{ln} = \frac{-1-0}{2-0}\\m_{ln} =-1/2\\$

For the slope of mn:

$m_{mn} = \frac{-1-2}{2-2}\\m_{ln} =-3/0 = \infty\\$

If any of the two lines is perpendicular, hence the triangle lmn is right-angled.

To check, we will take the product of the slopes and see if it is equivalent to -1.

Product of slope lm and ln

$m_{lm}\times m_{ln} = 1 \times -1/2\\m_{lm}\times m_{ln} = -1/2$

Since no product results in -1, hence δlmn is NOT a right triangle showing that Lydia's assertion is incorrect

Learn more on slopes here: brainly.com/question/3493733

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