Use the inverted pyramid method to derive the truth vlaue for the statement below assuming A and B are known to be true and X and Y are is known to be false: [~X v (~B v X)] v (~Y v A)

Below is one complete formal proof of validity. Copy the entire problem, and then provide the justification for each line in the proof (lines 3-6). 1. A • B2. (A v C) ⊃ D / ∴ A • D3. A4. A v C5. D6. A • D

Note: In this question there are two proofs. The total points you can earn for completing both proofs is 15 points. One proof will be worth 10 points and the other will be worth 5 points. Choose the point value you want me to use for each proof. If you do not specify a point value the first proof will be worth 10 points and the second proof will be worth 5 points. 1. Construct a formal proof of validity for the following argument. Note: Just three more lines are needed. Be sure to put the number of the line you are justifying and the rule of inference which justifies that line so I can verify the accuracy of your response:(Hint: Begin the proof by adding the three lines and putting the conclusion on the last line.)A ⊃ BC ⊃ DE ⊃ (A ∨ C)E∴B ∨D{“version”:”1.1″,”math”:”A ⊃ BC ⊃ DE ⊃ (A ∨ C)E∴B ∨D”}2. Construct a formal proof of validity for the following argument. Be sure to put the number of the line you are justifying and the rule of inference which justifies that line so I can verify the accuracy of your response:(Hint: The first line of your proof should be Addition of line 3.) (E ∨ F) ⊃ (G · H)(G ∨ H) ⊃ IE∴I{“version”:”1.1″,”math”:”(E ∨ F) ⊃ (G · H)(G ∨ H) ⊃ IE∴I”}

How does poor energy transmission across trophic levels likely contribute to many top-level predators’ normally high endangerment status? 

A population of mice has an annual per capita birth rate of 0.06 and an annual per capita death rate of 0.02. Estimate the number of individuals added to (or lost from) a population of 2,000 individuals in one year. 

Researchers discovered a nearly complete human-like skeleton on the island of Flores that is believed to be ~18,000 years old.  The features of this skeleton are similar to those of Homo erectus (an ancestral human) and to those of modern humans (Homo sapiens).  However, the Flores skeleton is much smaller in size than either of the other species and has a much smaller brain cavity.    In the statements below, which number matches the TEST that the scientists performed?   1. Based upon these and other differences, some scientists believe that the Flores skeleton is that of a previously undiscovered extinct species of human, which they have nicknamed “The Hobbit.”    2. Other scientists have suggested that the Flores skeleton is really an example of a modern human who suffered from microcephaly (a genetic disease physically characterized by unusually small sized skulls and underdeveloped brains).    3. Scientists used 3D computer imaging to compare different regions of the brain cavity of the Flores skeleton with those of modern humans from 9 individuals with microcephaly and 10 individuals with “normal” brains.    4. If the Flores skeleton was indeed that of a modern individual with microcephaly, then the brain cavity of this skeleton should be most similar to those of individuals known to have microcephaly.    5. However, the comparisons showed that the brain of the Flores skeleton was far more developed than individuals with microcephaly, yet certain regions of the Flores brain cavity were also significantly different from those of individuals with “normal” brains.  As such, the researchers concluded that the Flores skeleton represents a different species from modern humans.

You toss a two-sided coin four times in a row. If there is an equal chance of the coin landing on “heads” or “tails” for each toss, what is the probability of the following outcomes all happening in the order given? 1st toss: heads 2nd toss: tails 3rd toss:  tails 4th toss: heads

A friend of yours, Bob, has Huntington’s Disease (a dominant genetic disorder).  He inherited the disease from his mother; his father never expressed Huntington’s Disease.  Bob’s partner Barbara does not have the disease.  If Bob and Barbara have a baby together, what is the probability that the baby will have Huntington’s Disease?  

In this type of scientific thinking, you draw specific conclusions from general premises or ideas (it’s also know as top-down reasoning).  An example of this is found in cancer biology, where researchers within the last several decades have realized that the principle of evolution by natural selection helps to explain how malignant tumors develop resistance to chemotherapy drugs over time and repeated exposure.

The pedigree below shows a family with a history of an X-linked recessive disorder, hemophilia. The newlywed couple (individuals 1 and 2) are expecting a baby – which they know to be a boy.  Based upon their family history, they consult a genetic counselor to find out what the chances will be that their son will have hemophilia.  They discover that the mother is a carrier but that the father does not carry the condition.  Use your knowledge of pedigrees and probability to calculate the odds that the baby boy will inherit hemophilia: