1. Given the statements

"If I play hockey, then I am sore."

"I use the whirlpool if I am sore"

"I did not use the whirlpool"

Modus Tollens is used to arrive at the conclusion that I did not play hockey. T or F?

2.) Determine whether the argument is valid:

If George does not have eight legs, then he is not a spider

George is a spider

Therefore, George has eight legs

A.) Modus tollens; invalid

B.) Modus tollens, valid

3.) Given the argument

"All movies produced by John Sayles are wonderful"

"John Sayles produced a movie about coal miners"

"Therefore, there is a wonderful movie about coal miners"

p(x) x is a movie produced by Sayles

q(x) x is a movie about coal miners

r(x) movie x is wonderful

Identify the rule of inference used to arrive at statements p(x) and q(x) from the statements p(x) ^ q(x)

A. Modus tollens

B. Hypothetical syllogism

C. Conjunction

D. Simplification

4.) Given C(x,y) mean that person x has chatted with person y. Express the statement "There is a student in this class who has chatted with exactly one other student using quantifiers.

5.) Given E(x,y) mean that person x has sent e-mail to person y. Express the statement "No student in this class has sent email to exactly two other students in this class" using quantifiers.

6.) Let Q(x,y) be the predicate that x has taken y, where x ranges over students in this class and y ranges over math classes at this school. Express the statement "Every student in this class has taken exactly two math classes at this school" using quantifiers. Then, form the negation of the statement so that no negation is to the left of the quantifier. Express the negation in simple english.