Prove, or provide a counterexample to disprove, the following statement:             “The function f : ℝ ⟶ ℤ, defined by f(x) = ⌊ x + 2 ⌋  is onto.” Notice the use of the floor function in the definition of function f.  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 special symbols, instead of using the floor symbols in the function definition ⌊ x + 2 ⌋ you may use the expression ‘floor of ( x + 2 )’.

If 2 is the square of a positive integer, 0 > 1.

Let Ak  = { x ∈ ℝ | k-1 ≤  x  ≤ k }, for each positive integer k.  What is ?

For all sets A and B, if A ⊂ B, then A ∩ B = A.

Consider the following statement: “The function f : ℤ+ ⟶ ℝ defined by f(x) = 1/x is injective (one-to-one).” What must you demonstrate to prove the statement?  [Prove] What must you demonstrate to disprove the statement?  [Disprove]

The function f : ℤ ⟶ ℝ defined by f(x) = 1/x2 is injective (one-to-one).

Let Ak  = { x ∈ ℝ | k-1 ≤  x  ≤ k }, for each positive integer k. What is ?

Pertaining to the image, which carpal is outlined?                  

How many degrees is a hand rotated for an oblique position?

To ensure proper positioning of the elbow in the lateral projection, the: