Discrete Mathematics for Computer Science - UH

=?.

!I.

1?.

|~ilH

Terms

xe A xf A Ix x E A and P(x)} N

2 Q R A= B AC B Ag B AC B A5 B b=?a a b AUB AFnB UX nX Um Xi nt=Mxi A- B A A DB P(X) Xx Y x Ay x v y -x T I JAI

Si

Meaning

Sets, Proof Templates, and Induction

x is an element ofA x is not an element ofA Set notation Natural numbers

Integers Rationals

Real numbers Sets A and B are equal A is a subset of B A is nota subset of B A is a proper subset of B A is nota proper subset of B bimplies a a if and only if b A union B A intersect B Generalized union of family of sets X Generalized intersection of family of sets X XmU ... UXn Xm n ... nXn Elements of A not in B Elements not in A (A U B) - (A n B) Power set of X Product of X and Y Meet ofx and y Join ofx and y Complement of x Top Bottom Cardinality of A a,, + "-".+ a,,

Section

1.1 1.1 1.1 1.1.1l

1.1.1 1.1.1 I.1.1 1.1.3 1.1.5 1.1.5 1.1.5 1.1.5 i.1.5 1.1.5 1.3.1 1.3.1 1.3.1 1.3.1 1.3.1 1.3.1 1.3.2 1.3.2 1.3.2 1.3.4 1.3.4 1.3.5 1.3.5 1.3.5 1.15 1.3.5 1.5.1 1.7.1

Terms

"--p

pAq

pvq p q p q S X P 3 AKP (Vx)P(x) (3x)P(x) (VxE V)P(x) (3x E V)P(x)

A[i . .j]

1 V

4,

(x, y) E R or xRy R-1 RoS R+ R* n =-m(modp) Idx Lex Gtx Gex [x] min R D. S

Meaning

Formal Logic

Not p

p and q

p or q p implies q p is equivalent to q S logically implies X Conjecture about complexity For all x, P(x) There exists an x such that P(x) For all X EV, P(x) There exists an x E V such that P(x) Array with elements Ail, ... , A[j] Sheffer stroke Exclusive or Pierce arrow x is R-related to y The inverse of the relation R Composition of relations R and S U?? Ri URO R' n - m = kp for some k E N Identity relation Less than or equal relation Greater than relation Greater than or equal relation Equivalence class of x m divides n Equijoin of relations R and S

Section

2.1

2.1

2.1 2.1 2.1 2.3.3 2.5.6 2.7.2 2.7.2 2.7.3 2.7.3 2.7.3 2.4 2.4 2.9 3.1 3.2.1 3.2.2 3.4.4 3.4.4 3.6 3.1 3.1 3.1 3.1 3.6 3.8.1 3.10.2



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