Question

4 Inference proofs

Use laws of equivalence and inference rules to show how you can derive the conclusions from the given premises. Be sure to cite the rule used at each line and the line numbers of the hypotheses used for each rule.

a) Givens:

1 a∧b

2 c → ¬a

3 c∨d

Conclusion: d

b) Givens

1 p→(q∧r)

2 ¬r

Conclusion ¬p

Answer #1

Derive the conclusions from the premises in the arguments below
by utilizing inference rules: [45-3] C: ~(A V C) 1: A -> B 2: C
-> D 3: (B V D) -> E 4: ~E

4. Use inference and equivalence rules to determine what
conclusion (if any) can be reached from the following paragraph?
First identify your atomic propositions and write each statement as
a WFF.
“You will not get infected by the virus if and only if you
observe social distancing guidelines. If you observed social
distancing guidelines then you are not partying. You are partying
or you are not wearing a face mask. If you are infected by the
virus then you are...

Write down the inference or replacement rule and the line(s) it
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(1) A -> [(AvB) -> (C•D)]
(2) [A • (AvB)] -> (C•D) ______
(1) (A • B) v (~A • B)
(2) (~A • B) v (A •B) _________
(1) (P • Q)
(2) (P • Q) -> ~ (A v B)
(3) ~ (A v B) _________
1) A• (B v C)
(2) [A• (B v C)] v [~A• ~(B v C)] ___________
(1) (A•B) ≡ (C•D)...

Derive the following using all known inferences rules and
equivalences
including QE.
Remember that equivalences afford you greater power than
derivation rules, because
you are permtted to substitute equivalent sub formlas within a wff.
For example, all the
moves on the left below are legitimate inferences even though the
first conditional is the
main operator. However, it is important to remember that you must
always be operating
on a true self-contained wff. The moves on the right are not
legitimate...

4. When the second derivative test (SDT) is used for a critical
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cos(x) with domain restricted to {(x, y) | −1 ≤ x ≤ 4 and − 2 ≤ y ≤
4} and the three points P = ( π/2 , 0) Q = (0, 1) and R = (π,
−1).
(a) Find all the critical points...

4. When the second derivative test (SDT) is used for a critical
point the result can be local maximum, local minimum, saddle point
or test inconclusive. Consider the function f(x, y) = y 2 − 2y
cos(x) with domain restricted to {(x, y) | −1 ≤ x ≤ 4 and − 2 ≤ y ≤
4} and the three points P = ( π 2 , 0) Q = (0, 1) and R = (π,
−1).
(a) Find all the...

USE CALCULATOR AND SHOW FULL STEPS FOR EACH TEST INCLUDING WHAT
YOU INPUT Below are random samples of enrollments for medical
schools that specialize in research and for those that specialize
in primary care. Is there a difference in the average enrollment
for the two specializations? Use a significance level of a =
0.05.
a) Give the name of the hypothesis test that would be
appropriate for this situation. (1 point)
b) State the hypotheses in symbols. (2 points)
c)...

For each of the following cases a-e, you will use the Supply
& Demand theory and model to determine what will happen to the
equilibrium price (P*) and equilibrium quantity (Q*). Explain how
you reach your conclusions by following the 4 steps below (in that
exact order) for each case a, b,....: Be neat! Do not clump all
your answers together.
1. Among all the variables/determinants that shift the curves,
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microeconomics
note: briefly show how you get the result.
Assume that the table below describes the production
possibilities confronting an economy. Using that information:
Potential output combinations
Convenience Stores
Homeless Shelters
A
0
22
B
1
18
C
2
13
D
3
7
E
4
0
1. Draw the production-possibilities curve. Be sure to label
each alternative output combination
(A through E). (Note: put # of convenience stores on the horizontal
line)
2. Calculate the opportunity cost of building the...

Hello if you could please show work for the problems and show
the necessary r code for questions b and c I would appreciate it.
Thank you
A shoe manufacturer compared material A and material B for the
soles of shoes. Twelve volunteers each got two shoes. The left was
made with material A and the right with material B. On both shoes,
the material was 1 inch thick. Volunteers used the shoes normally
for two months and returned them...

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