{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HM1-Review-Answers - CS 341 Homework 1 Answers 1 Prove each...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
CS 341 Homework 1 Answers 1) Prove each of the following: a) (( A B ) C ) ( ¬ A ¬ B C ). (( A B ) C ) ( ¬ A ¬ B C ) ( ¬ ( A B ) C ) ( ¬ A ¬ B C ) Definition of (( ¬ A ¬ B ) C ) ( ¬ A ¬ B C ) de Morgan’s Law ( ¬ A ¬ B C ) ( ¬ A ¬ B C ) Associativity of True Definition of b) ( A ¬ B ¬ C ) ( A ¬ ( B C )). ( A ¬ B ¬ C ) ( A ¬ ( B C )) ¬ ( A ¬ B ¬ C ) ( A ¬ ( B C )) Definition of ¬ A B C ( A ¬ ( B C )) de Morgan’s Law ¬ A B C A ¬ ( B C ) Associativity of ¬ A B C A ¬ B ¬ C de Morgan’s Law ¬ A A B ¬ B C ¬ C Commutativity of ( ¬ A A ) ( B ¬ B ) ( C ¬ C ) Associativity of True True True Definition of True Definition of 2) List the elements of each of the following sets: a) P ({apple, pear, banana}). , {apple}, {pear}, {banana}, {apple, pear}, {apple, banana}, {pear, banana}, {apple, pear,banana} b) P ({ a , b }) - P ({ a , c }). { b }, { a , b } c) P ( ). d) { a , b } × {1, 2, 3} × . e) { x : ( x 7 x 7}. 7 f) { x : 5 y ( y < 10 ( y + 2 = x ))} (where is the set of nonnegative integers). 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 g) { x : 5 y ( 5 z   (( x = y + z ) ( y < 5) ( z < 4)))}. 0, 1, 2, 3, 4, 5, 6, 7 3) Prove each of the following: a) A ( B C D ) = ( A B ) ( A D ) ( A C ). A ( B C D ) = ( A B ) ( A D ) ( A C ). Set union distributes over set intersection.
Image of page 1

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

View Full Document Right Arrow Icon
4) Consider the English sentence, “If some bakery sells stale bread and some hotel sells flat soda, then the only thing everyone likes is tea.” This sentence has at least two meanings. Write two (logically different) first-order- logic sentences that correspond to meanings that could be assigned to this sentence. Use the following predicates: B ( x ) is True iff x is a bakery; S B ( x ) is True iff x sells stale bread; H ( x ) is True iff x is a hotel; S S ( x ) is True iff x sells flat soda; L ( x , y
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern