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Prove, or provide a counterexample to disprove, the following statement:             “The function f : ℕ ⟶ ℕ  be defined by f(n) = n2 + 5  is onto.” Use good proof technique. Grading rubric:1 pt. State the definition of onto at the beginning, then prove or 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.

The term cyanosis refers to what?

Consider proving the following statement using a proof by cases. “For all integers n, n ≤ n2.” What 3 cases do you use for this proof?  [Cases] What do you demonstrate must be true to complete the proof of each case?  [Prove]

A ____ connects all the computers in a system.

For all sets A and B, if sets A and B are not disjoint, A – B = A.

Compared to a low ratio grid, a high ratio grid will1.  absorb more primary radiation2.  absorb more scattered radiation3.  allow less centering latitude

Prove the following statement using a direct proof. “For all integers m and n, if m is odd and n is even, then (m n) is even.” Use good proof technique.   Grading rubric:1 pt. State what is given and assumed true to begin.1 pt. Clearly explain your steps.1 pt. State the final conclusion at the end of the proof.

Prove the following statement using induction. “For all integers n ≥ 2, n2 ≥ n+1. ”  Use good proof technique.  Grading rubric:1 pt. State the basis step, then prove it.1 pt. State the inductive hypothesis.2 pt. Complete the proof of the inductive step.1 pt. State the final conclusion at the end of the proof.1 pt. Label each part: the basis step, inductive hypothesis, inductive step, and conclusion. Note: To avoid the need for typing superscript exponents, you may use the expression ‘n^2’ to represent n2.  Also the ≥ symbol can be written as >=.

For all sets A, B, and C, A ⋂ (B ⋃ C) = (A ⋃ B) ⋂ (A ⋃ C).

The membership table in the previous problem shows that the two given sets [NEQ] equal.