{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework 2 Solutions

# Homework 2 Solutions - 1.4 Problem 9(a xL(x Jerry(b xyL(x...

This preview shows pages 1–2. Sign up to view the full content.

§ 1.4 Problem 1 ( a ): “For every number x , there is a bigger number y .” ( b ): “For any two numbers x and y , if x and y are nonnegative then so is their product.” ( c ): “For any two numbers x and y , there is another number z that is equal to their product.” § 1.4 Problem 9 ( a ): xL ( x, Jerry) ( b ): x yL ( x,y ) ( c ): x yL ( y,x ) ( d ): ¬∃ x yL ( x,y ) ( e ): x ¬ L (Lydia ,x ) ( f ): x y ¬ L ( y,x ) ( g ): x y ( x = y ) ( zL ( z,y )) ( h ): x y ( ( x negationslash = y ) ∧ ∀ z ( x = z x = y ) L (Lynn ,z ) ) ( i ): xL ( x,x ) ( j ): x y ( x negationslash = y ) → ¬ L ( x,y ) The book gives the inequivalent solution x y ( L ( x,y ) x = y ) . This says that everyone loves them- selves and nobody else, whereas my solution allows for the possibility that people might not love themselves. It is unclear from the English which is intended. § 1.4 Problem 12 ( e ): ( x ( x negationslash = Joseph) C (Sanjay ,x ) ) ( f ): x ¬ I ( x ) ( g ): ¬∀ xI ( x ) ( h ): x y ( ( x = y ) I ( y ) ) ( i ): x y ( ( x negationslash = y ) I ( y ) ) ( j ): x ( I ( x ) → ∃ y ( ( y negationslash = x ) C ( x,y ) )) ( k ): x ( I ( x ) ∧ ∀ y ( ( y negationslash = x ) → ¬ C ( x,y ) )) ( l ): x y ( ( x negationslash = y ) ∧ ¬ C ( x,y ) ) ( m ): x yC ( x,y ) ( n ): x y z ( ( x negationslash = y ) ∧ ¬ C ( x,z ) ∧ ¬ ( y,z ) ) ( o ): x y bracketleftbig ( x negationslash = y ) ∧ ∀ z ( C ( x,z ) C ( y,z ) )bracketrightbig Some of these are open to interpretation, due to the vagueness of the English language. For instance, take part ( n ), for which the solutions manual gives x y ( x negationslash = y ∧ ∀ z ¬ ( C ( x,z ) C ( y,z ) )) My solution says, “There are two people x and y and a person z with whom x and y have not chatted,” so that x and y have not chatted with the same person. The solutions manual’s solution says, “There are two

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern