ECS 20 Midterm Exam, Nov.1, 2011, Solutions
1. What is the truth value of (p q ) (p q ) when both p and q are false?
Ans: When p and q are both false, so are (p q ) and (p q ). Hence (p q ) (p q ) is true.
2. Determine the truth value of each statement. T
ECS20 Handout 4
Oct 12, 2010
1. A set is an unordered collection of distinct objects. Notation A, B, C, . . . . Duplicate elements only count once, e.g. if a = b then A = cfw_a, b, c = cfw_a, c.
2. The objects in a set are also called the elements, or mem
Quiz2 - 03/6/07
Part I
Question a) Let P (n) be the proposition: 12 + 32 + . . . + (2n 1)2 = We want to prove that P (n) is true, for all N 1. n(2n 1)(2n + 1) For sake of clarity, we call LHS(N ) = 12 + 32 + . . . + (2n + 1)2 and RHS(N ) = . 3 Basic step:
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ECS 20: Discrete Mathematics Quizz 1 January 25, 2007
Notes: 1) 2) 3) 4) 5) 6) quizz is open book, open notes. No computers though. You have 40 minutes, no more: I will strictly enforce this. You can answer directly on these sheets (preferre
Quiz 1 - on 01/25/2007 Part I
Question 1
We want to check the nature of the statement (p q ) (p r) (q r): Using a truth-table: p T T T T F F F F q T T F F T T F F r T F T F T F T F pq T T F F T T T T p r T T T T T F T F a = (p q ) (p r) T T F F T F T F qr
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Midterm - 02/15/07
Part I
Exercise 1 a) Truth table for A = [(p q) (p r) (q r)] r: p T T T T F F F F q T T F F T T F F r T F T F T F T F pq T T T T T T F F pr T F T F T T T T qr T F T T T F T T [(p q) (p r) (q r)] T F T F T F F F A T T T T T T T T
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ECS 20: Discrete Mathematics Midterm February 15, 2007
Notes: 1) 2) 3) 4) 5) 6) Midterm is open book, open notes. No computers though. You have one hour, no more. You can answer directly on these sheets (preferred), or on loose paper. Please
(c)2001-2003, Michael P. Frank
Rosen 2.1-2.2
The Theory of Sets
2
(c)2001-2003, Michael P. Frank
3
A set is a new type of structure, representing an
unordered collection (group, plurality) of zero or
more distinct (different) objects.
Set theory deals w
mcs 2012/1/19 21:32 page i #1
Mathematics for Computer Science
revised Thursday 19th January, 2012, 21:32
Eric Lehman
Google Inc.
F Thomson Leighton
Department of Mathematics
and the Computer Science and AI Laboratory,
Massachussetts Institute of Technolo