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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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The professor informs the class that there will be a test next week. what is the probability that a randomly selected student st

marusya05 [52]

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<h3>How to calculate the probability?</h3>

In this exercise, you're required to determine the probability that students who were randomly selected studied for the test, if they pass it with a B or higher grade. Thus, we would apply Bayes's theorem.

Let S represent studied for.

Let B represent a score of B or higher grade

Therefore, we need to find P(S|B):

$S|B = \frac{B|S \times S}{B|S \times S\; +\; B|S' \times S'} \\\\S|B = \frac{0.55 \times 0.6}{0.55 \times 0.6 \;+ \;0.2 \times 0.4}\\\\S|B =\frac{0.33}{0.33 + 0.08} \\\\S|B =\frac{0.33}{0.41}$

S|B = 0.80.

Read more on probability here: brainly.com/question/25870256

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<u>Complete Question:</u>

At the beginning of the semester, a professor tells students that if they study for the tests, then there is a 55% chance they will get a B or higher on the tests. If they do not study, there is a 20% chance that they will get a B or higher on the tests. The professor knows from prior surveys that 60% of students study for the tests. The probabilities are displayed in the tree diagram.

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