Which method of proof would be the best choice for proving the following claim? Claim: For all positive integers m{“version”:”1.1″,”math”:”m”} and n{“version”:”1.1″,”math”:”n”}, if mn≥65{“version”:”1.1″,”math”:”mn≥65″}, then m>8{“version”:”1.1″,”math”:”m>8″} or n>8{“version”:”1.1″,”math”:”n>8″}.

Simplify the proposition ¬∃x(Z(x)∧¬R(x)){“version”:”1.1″,”math”:”¬∃x(Z(x)∧¬R(x))”} by moving the negation symbol as far inside the parentheses as possible.  Show all work on paper.  When you are finished, type “done” in the space below.

Let R(x) = “x is a rational number” and let Z(x) = “x is an integer”.  The domain of x is the real numbers.  Match each proposition below with its English translation.  Not all translations will be used.  

Free point (pick TRUE)

An avulsion fracture, Jones fracture, and stress fracture are the three most common types of fractures sustained by this bone.

High heat and high pressure without full melting will lead to ________ rocks.

A patient has a family history of colorectal cancer. Which of the following is the most important screening recommendation for this patient?  

If concussion symptoms increase during the return to play progression, the patient must rest for 24 hours and restart the return to play process from stage 1.

A project network is shown below.       The time required for each activity is shown in the table. Activity Time(days) A 4 B 9 C 5 D 5 E 10 F 6 G 5 Formulas   a. What is the critical path? (3 points) b. What is the length of the project? (3 points)   c. What is the slack of Activity C? (2 points)  d. What is the slack of Activity E? (2 points)  

What are Hamlet’s hopes about death in his soliloquy?