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Exam in Discrete Mathematics ANSWERS

11-Jun-2014 Is the compound proposition in question 1 a tautology? Answer: No. a b c d e f g h i j k m n. Figure 1: A graph G considered in Exercise 6 ...



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PDF Discrete Mathematics - Question Papers

Computer Science. Paper 105 T - DISCRETE MATHEMATICS. Time: 3 Hours]. [Max. Marks: 100. Instructions to Candidates: Answer all Sections. SECTION-A.



Part A - Questions and Answers

Discrete Mathematics. Question 9: Find the idempotent elements of. {1 1

Discrete Mathematics for Computer Science

I. =ý. 1. !

|~ilH

Terms Meaning Section

Sets, Proof Templates, and Induction

x e A x is an element ofA 1.1 x f A x is not an element ofA 1.1

Ix x E A and P(x)} Set notation 1.1

N Natural numbers 1.1.1l

2 Integers 1.1.1

Q Rationals 1.1.1

R Real numbers I.1.1

A = B Sets A and B are equal 1.1.3

A C B A is a subset of B 1.1.5

A g B A is nota subset of B 1.1.5

A C B A is a proper subset of B 1.1.5

A 5 B A is nota proper subset of B 1.1.5

b=a bimplies a i.1.5 a b a if and only if b 1.1.5

AUB A union B 1.3.1

AFnB A intersect B 1.3.1

UX Generalized union of family of sets X 1.3.1

nX Generalized intersection of family of sets X 1.3.1

Um Xi Xm U ...UXn 1.3.1

nt=Mxi Xm n ... n Xn 1.3.1

A -B Elements of A not in B 1.3.2

A Elements not in A 1.3.2

A D B (A U B) -(A n B) 1.3.2

P(X) Power set of X 1.3.4

X x Y Product of X and Y 1.3.4

x A y Meet ofx and y 1.3.5 x v y Join ofx and y 1.3.5 -x Complement of x 1.3.5

T Top 1.15

I Bottom 1.3.5

JAI Cardinality of A 1.5.1

Si a,, + " -". + a,, 1.7.1

Terms Meaning Section

Formal Logic

"--p Not p 2.1 pAq p and q 2.1 pvq p or q 2.1 p q p implies q 2.1 p q p is equivalent to q 2.1

S X S logically implies X 2.3.3

P 3 AKP Conjecture about complexity 2.5.6

(Vx)P(x) For all x, P(x) 2.7.2 (3x)P(x) There exists an x such that P(x) 2.7.2 (VxE V)P(x) For all X EV, P(x) 2.7.3 (3x E V)P(x) There exists an x E V such that P(x) 2.7.3

A[i ..j] Array with elements Ail, ..., A[j] 2.7.3

1 Sheffer stroke 2.4

V Exclusive or 2.4

4, Pierce arrow 2.9

(x, y) E R or xRy x is R-related to y 3.1

R-1 The inverse of the relation R 3.2.1

RoS Composition of relations R and S 3.2.2

R+ U°° Ri 3.4.4

R* URO R' 3.4.4

n =- m(modp) n -m = kp for some k E N 3.6

Idx Identity relation 3.1

Lex Less than or equal relation 3.1

Gtx Greater than relation 3.1

Gex Greater than or equal relation 3.1

[x] Equivalence class of x 3.6 min m divides n 3.8.1

R D. S Equijoin of relations R and S 3.10.2

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Changing the way the world learns

Discrete Mathematics

for Computer Science fo Copue Science

Gary Haggard

Bucknell University

John Schlipf

University of Cincinnati

Sue Whitesides

McGill University

THOrVIMSO3N

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