Ncghost210

Dec 8, 2011, 08:11 PM

Greetings MacRumors. I am a TA for a University in North Carolina and the professor for the class I am assisting has given the students the following assignment that they are to turn in to me to check tomorrow. Problem is, the professor has now left on vacation and did not give me an answer key for the problems. Even better, I have no formal training in the matter of formalization of logic equations.

If someone could help I, and the students, would greatly appreciate it as they will get their grades back quicker. Thank you for any help or even just a point in the right direction.

Translation scheme:

Nx: x is a number

Ox: x is odd

Ex: x is even

Lxy: x<y

Bxyz: x is between y and z

s(x)= the successor of x

p(x,y)=x (multiplication symbol) y

c(x)=x^3

r=Rachel’s favorite number

1. A number is odd unless it is even.

2. Every number is even or odd, but no number is both even and odd.

3. The cube of Rachel’s favorite number is even.

4. The product of any two numbers is less than the product of their successors.

5. The successor of Rachel’s favorite number is between Rachel’s favorite number and its cube.

6. Every number other than Rachel’s favorite number is less than its square.

7. The square of every number is less than its cube.

8. The product of Rachel’s favorite number and its successor is less than its cube.

9. The cube of every number greater than Rachel’s favorite number is odd.

10. Rachel’s favorite number is not the only number the cube of whose square is greater than Rachel’s favorite number.

If someone could help I, and the students, would greatly appreciate it as they will get their grades back quicker. Thank you for any help or even just a point in the right direction.

Translation scheme:

Nx: x is a number

Ox: x is odd

Ex: x is even

Lxy: x<y

Bxyz: x is between y and z

s(x)= the successor of x

p(x,y)=x (multiplication symbol) y

c(x)=x^3

r=Rachel’s favorite number

1. A number is odd unless it is even.

2. Every number is even or odd, but no number is both even and odd.

3. The cube of Rachel’s favorite number is even.

4. The product of any two numbers is less than the product of their successors.

5. The successor of Rachel’s favorite number is between Rachel’s favorite number and its cube.

6. Every number other than Rachel’s favorite number is less than its square.

7. The square of every number is less than its cube.

8. The product of Rachel’s favorite number and its successor is less than its cube.

9. The cube of every number greater than Rachel’s favorite number is odd.

10. Rachel’s favorite number is not the only number the cube of whose square is greater than Rachel’s favorite number.