Problems Sets Quizzes 1-8

Discrete Mathematics and Its Applications with MathZone

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

View Full Document Right Arrow Icon
ICS.6D, Fall 2007, Quiz 1, October 8, 2007 1) Determine whether each of these statements is T rue or F alse, by circling the correct answer: If 5=5, then 10=10 T or F If 5=5, then 10=749 T or F If 5=0, then 10=10 T or F If 5=0, then 10=749 T or F 2) a) Write the truth table for the following proposition: ( p V q ) ¬ p . (Extra columns have been provided for your work. Please label those you use.) An s: p ( p V q ) → ¬ p b) Using the above table, decide if the following is a tautology , contradiction , or contingency : ( ( p V q ) ¬ p) ¬ p : ______________ 3) Determine the truth value of each statement below, assuming the domain is integers : 5 x (x > 6) _________________ 2200 x (x > 6) _________________ 2200 x 5 y (y > x) _______________ 5 x 2200 y (y > x) __________________ 4) Let L(x) = “x loves Larry”, and let J(x) = “x loves Jerry”. Express the following statements using quantifiers and predicates L(x) and J(x): a) “Some people love Larry and some people love Jerry.” : __________________ b) “Some people love Larry but don’t love Jerry.” : __________________ c) “Everyone who loves Larry must also love Jerry.” : __________________
Background image of page 1

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

View Full DocumentRight Arrow Icon
d) “If everyone loves Larry then everyone loves Jerry.” : __________________ ICS.6D: Discrete Mathematics For Computer Science, Fall 2007, Quiz 2 1) Label each of the following T rue or F alse: {1} {1} ____, {1} {1} ____, {1} {1} ____, [21pts] {1} ___, {1} ____, {1} ____, { } ____ 2) [21pts] If A = {s, t, t, q, r, t, q} and B = {t, v, t}, then |A| = ______, |P(A)| = __________, |A × B| = ________ A B = _________________________ A – B = ______________________________ A B = _________________________________________, {r,s,r} × B = ______________________________________ 3) [12pts ] Compute the following values: - 4.3 = _______ 4.3 = ________ 4/3 = _______ - 4/3 = ________ 4) [20pts] State whether each of these functions from Z to Z ( Z =Integers ) is I njective (one-to- one ), S urjective (onto ), B ijective, or N either, and briefly explain/justify each answer. f(n) = 5n+1 ___________________________________________________________ f(n) = n 2 - 4 ___________________________________________________________ f(n) = n / 5 ___________________________________________________________ f(n) = 5 - n ____________________________________________________________ 5) [26pts] Prove the following claim (for any sets A and B): A (B - A) Do it on the next page where we list several facts that can be useful in this claim. You don’t have to use all the facts listed or explain which of the stated facts you are using. We’ll give partial credit if some part of your argument is correct and other part is not.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This homework help was uploaded on 01/30/2008 for the course ICS 6D taught by Professor Jarecki during the Fall '07 term at UC Irvine.

Page1 / 14

Problems Sets Quizzes 1-8 - ICS.6D, Fall 2007, Quiz 1,...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online