Alex
Alex
Bonnie
Bonnie
EE 3752
Colin
Colin
Danielle
CSC 3102 Danielle
Earl
Earl
ECE
CSC
ME
EE 4740
Fiona
Fiona
Gaston
Gaston
Math
:
!
Alex
ECE
Bonnie
8 2
( )2
Colin
( )=
CSC
Danielle
ME
Earl
Fiona
Math
Gaston
cfw_
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:
!
Alex
ECE
Bonnie
8 2
( )2
EE 4740Spring 2016
Predicates and Quantiers
Sections 1.4 and 1.5
January 25, 2016
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Predicates
Every computer at LSU is secure
(ECE1 is secure) and (ECE2 is secure)and (CSC1 is
secure) and (ECE5 is secure) and (CSC3 is secure)
Simi
EE 4740Spring 2016
Proofs
Sections 1.7 and 1.8
January 25, 2016
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Theorem, Lemmas and Corollaries
A theorem is a statement that can be shown to be true
A proof of the theorem is a valid argument that (uses the
given axioms, postula
EE 4740Spring 2016
Propositional Logic
Sections 1.11.3
January 20, 2016
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Logic
EE 2740: Design digital circuits
EE 4740: Construct valid arguments (reasoning)
EE 4740Spring 2016
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Logic
EE 2740: Design digital circuits
EE 474
EE 4740Spring 2016
Rules of Inference
Section1.6
January 11, 2016
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Proofs and Fallacies
A proof is a valid argument
An argument is a sequence of statements from premise to
conclusion.
An argument is valid if the reasoning follows
EE 4740Spring 2016
Sequences and Summations
Section 2.4
February 22, 2016
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Sequences
A sequence (or progression) is an ordered list of quantities
(say from a set S)
: Z+ S
Formally, a sequence is a function f
So the sequence can
EE 4740Spring 2016
Countability
Section 2.5
February 22, 2016
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Cardinality Revisited
|A| = |B |
iff
there exists a bijection f
Set S is countable or enumerable
|S | is nite,
For innite countable sets S, there is a bijection f
1
(or
EE 4740Spring 2016
Mathematical Induction
Section 5.15.2
March 2, 2016
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The Approach
where n, n0
Z+
Base Step: Prove that P (n0 ) is true
Induction Hypothesis: Assume P (n) to be true for n
n0 ,
You need to prove that
n n0
P (n)
EE 4740Spring 2016
Relations
Section 9.19.4
March 14, 2016
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(Binary) Relations
A (binary) relation from set A to set B is R
EE 4740Spring 2016
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AB
(Binary) Relations
A (binary) relation from set A to set B is R
Alex
Bonnie
E
EE 4740Spring 2016
Graphs: The Basics
Section 10.110.3
April 8, 2016
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Graphs
Graphs express relationships between objects
edges
G
vertices or nodes
= (V , E )
In its basic form, a directed graph (or digraph) is a relation
E
V V
un
EE 4740Spring 2016
Equivalence Relations and
Partitions
Section 9.5
March 30, 2016
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Reexive Relation
R
A A is reexive
iff
=
(is equal to)
(is greater than or equal to)
m
a A,
(is equivalent to (modulo m)
is a friend of
is a s
Quiz 3: February 29, 2016
Let A = cfw_0, 1 and Let C = cfw_0, 1, 2, 3. Prove the following
function to be injective.
f : A A C,
with (a, b) A A, f (a, b) = 2a + b
Hint: observe that if f (a1 , b1 ) = f (a2 , b2 ), then a1 + b21 = a2 + b22 .
Consider the i
Quiz 2: February 15, 2016
Prove, without using a Venn Diagram, that the following
statement holds for any sets A, B, C.
(A B) (A C)
EE 4740Spring 2016
(B C)
F
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Quiz 2 Solution
This is the sets analog of the statement if Quiz 1. That is, let
x A P, x B
Quiz 1: January 27, 2016
Without using a truth table, prove the following statement (to be
a tautology).
(P or Q) and (P or R)
= (Q or R)
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Quiz 1 (Direct) Solution
Let us assume that the premise or antecedent (left side of the
main