In: Advanced Math

Prove verbally without referencing a Venn diagram, can use a Vennn diagram to visually see it but cannot be a reference in proof.

a) Let A be a set. Prove that A*⊆* A.

b) Let A, B, and U be sets so that A *⊆* U and B
*⊆* U. Prove that A *⊆* B if and only if (U \ B)
*⊆* (U \ A)

c) Let A, B be sets. Prove that A *\* (A *∩* B) =
A \ B

d) Let A, B be sets. Prove that A *\* (B \ A) = A

Using only membership tables (i.e., without Venn diagrams or set
identities), prove or disprove that (? − ?) ∪ (? − ?) and ((? − ?̅)
− ?) ∪ (? ∩ ?̅) ∪ (? − (? ∪ ?)) are equivalent. Ensure that you
fill the table completely, even if you are disproving this
equivalence, and do not skip any columns.

2 cards are drawn without replacement from a standard deck. draw
a venn diagram that relates to the following:
1. Both cards are from the same suit
2. Both cards have the same rank
3. One card is a face card and the other card is a number
card
4. Both cards are from a red suit

Use the following Venn diagram tools to construct diagrams that
represent the given syllogistic forms from the Boolean standpoint.
Once you have constructed your diagrams, interpret them to
determine whether each syllogistic form is valid or invalid from
the Boolean standpoint. Indicate your answers using the dropdown
menus below each diagram.
Argument 1
Premise 1:
All O are E.
Premise 2:
All L are O.
Conclusion:
All L are E.
This syllogistic form is ________ from the Boolean
standpoint.
Argument...

Classical Mechanics problem:
See if you can prove the so-called virial theorem. This is a
statement that relates the average kinetic energy of a stable
system to the potential energy of the system. It applies when the
force between two particles of the system has a corresponding
potentual energy U of the form U = kr^n, where r is the separation
of the particles and n is some real number. So, suppose a mass m
moves in a circular orbit...

The phrase "when the tide goes out we can see who was swimming
without clothes" is an adage referencing which of the following
scenarios?
falling sea levels create trade shocks for countries heavily
reliant on fish industry
when capital inflows cease, current account deficits become
apparent
when excessively risky positions have been taken by banks
international capital exits rabidly
when GDP declines, households that have budgeted poorly become
apparent
The first of the East Asian Tigers to experience speculative
attack...

Henrietta Lacks we can see this illustrated in that
women cells were taken without her knowledge or permission and used
for technological and medical purposes was this right

what kinds of healthcare can an individual use without being
sick

Use the tree diagram technique that can be found in
Lecture 12 to solve this problem. Suppose that 50% of all people
who take a pregnancy test are, in fact, pregnant. A certain
pregnancy test is known to identify 95% of pregnancies with a
positive test result. However, 2% of people who are not pregnant
will have a positive test result.
Find the following probabilities:
a. What is the probability that someone is pregnant and
tests positive?
b. What is...

explain how a scatter diagram can be used to identify the type of
regression to use

Companies can use the WACC to see if the investment projects
available to them are worthwhile to undertake. How can the WACC be
both an average cost and a marginal cost? What tools are available
to us to determine the relationship between ROIC and WACC?

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