Prove, or provide a counterexample to disprove, the following statement:             “The function f : ℤ ⟶ ℕ defined by f(n) = n2 is a bijection.” Use good proof technique.  Remember that a bijection is both one-to-one (injective) and onto (surjective).  To prove, you must demonstrate both properties are true; to disprove, you only need a counterexample that shows one of the properties is not valid. Grading rubric:1 pt.  Indicate whether you will be proving or disproving the assertion.  Also, if proving, state both definitions, one-to-one and onto; if disproving, state the definition you plan to disprove.  1 pt.  State any givens and assumptions.1 pt.  Clearly explain your reasoning.1 pt.  Remember to state the final conclusion at the end of the proof. Note:  To avoid the need for typing superscript exponents, you may use the expression ‘n^2’ or ‘n-squared’ to represent n2.

What is the function of the fungal fruiting body?

When the chromosomes separate during mitosis this is known as which phase?

The main reason reptiles are so well-adapted to a land environment is their method of

Define S, a set of bit strings, recursively as follows. Initial Condition:  1 ∈ SRecursion: If m ∈ S then 1m ∈ S. Which of the following best describes set S?

With the universe of discourse for x as the set of all people alive in the world and the universe of discourse for y as the set of all countries in the world, we define the following predicates: F(x) is “x is a current FSU student,” G(x) is “x is a graduate of FSU,” and R(x, y) is “x is a resident of y.” Which of the following logical expressions accurately expresses this statement: Some graduates of FSU are not residents of the United States and some graduates of FSU are residents of the United States.

Which one of these is present in all fishes?

During this course, you have studied chemistry, physics, genetics, botany, biochemistry, microbiology, virology, ecology, biotechnology, and (oh yeah) biology.  Yes, you did all that.  Tell me the one lecture that will change how you will live differently after this class. Provide a detailed explanation of the reasons this made an impact for you.  Your answer must be at least 200 meaningful words.  If you skip this question, make your answer too short or too superficial, the rest of the exam WILL NOT COUNT.

Which one feature is believed to have been the first step in the evolution of land plants from the green algae?

Unicellular eukaryotes undergo mitotic division to