(1) Use quantifiers, logic symbols, and English to translate the following: (a) Every positive real number has a positive real square root. (b) Every negative integer does not have a real square root. (c) (3x)N(y)Nx+y=2 (d) (3x)N(Vy)Nx.y=0

Evaluate the following. (Remember to show your working, and give the exact answer.) (a) (24-5(-4)-(2-5)²)/(9-42) (b) √64+ (26-32+43)1/2/4

Show that each of the following is true. Give a property of addition to justify each step of your argument. a. x + (y+z) =z+ (x+y) b. x + (y+z)= y + (x+z)

John Wallis and other 17th century mathematicians were struggling with how to fit negative numbers into arithmetic without introducing inconsistencies. Explain the reasoning leading to Wallis's paradoxical claim that, if negative numbers are less than zero, they must be greater than infinity. Wallis's argument depends, in part, on the assertion that (3/-1) = -3. Must this be true? Why or why not? If a student proposed Wallis's argument, how would you respond?

17y+Sy+4 9y-By-1 20y+13y-15 20y+13y-15 ト+AS+A