.r. I
S
Q
onxvw w
33:8 an. agar?
\zxxcxxxgcxkvo 3,2»
wéwswm kQEV =3 \«Ka? K unxo K A
U Q - We %
in 1 w
{W «N
\$ \.U.N \vaQ
U tuna firi®é x 13.38 TEFEWN c
it? x
Nkinx» I mm Em! . up.
\ X\ W
3n? f . Re N
mgmiéwu Mnnw . {Tami u
Aw? U CURVY; 0C}
Math Induction
based on How to Prove It (chapter 6)
To prove a goal of the form n P( n):
First prove the base case:
P(n0) is true
then prove the induction step:
n n >n0 (P( n) P( n + 1).
Example 6.1.1. Prove that for every natural
number n, 20 + 21 + + 2
Combinatorial Structures
Introductory Lecture
Basic Notions
Combinatorics
is a branch of mathematicsconcerning the
study of countable or finite discrete
structures.
Discrete Structures:
abstract mathematical structures that
represent discrete objects and
Propositions
A proposition is a declarative sentence that is either true or
false.
Examples of propositions:
a) The Moon is made of green cheese.
b) Trenton is the capital of New Jersey.
Toronto is the capital of Canada.
d) 1 + 0 = 1
e) 0 + 0 = 2
c)
Examp
Proof Strategies
based on How to Prove It (chapter 3)
Few terms
A proof of a theorem is simply a deductive
argument whose premises are the
hypotheses of the theorem and whose
conclusion is the conclusion of the
theorem.
We will refer to the statements tha