**Discrete Mathematics Class Notes**
These comprehensive class notes cover all major topics in discrete mathematics, providing a thorough foundation for understanding the principles and applications of this field. The notes include detailed explanations, examples, and proofs, making them a valua...
statement proposition declarative sentence ,
either
True or False ,
but not both
eX .
p (denotation of a statement) : Discrete Math is a required
course for sophomores
Truth Values : True or False
r = 2 + 3 = 5
Truth Values : True or False
note :
Primitive statements simple statements cannot be simplified
we usually use small alphabets to denote primitive
statements
new statements can be constructed from primitive ones in
2
ways :
1 the negation of a primitive statement
p or ~p (read as "not p" (
2 form a compound statement by logic connections
I statements formed by logic connections
Compound statements from primitive statements (
·
conjunction :
(
""
"AND" (represented by
ex . p and 9 , p q
·
Disjunction :
""
"OR" (represented by (
ex . por g or both p q
,
·
Exclusive OR :
11
represented
"
by
ex . p or
a, ph
·
Implication :
11
represented
"
by p only if q
ex .
p implies & if p then a ,
p G /
p is sufficient (condition) for 9 9 is necessary
,
(result) for P
, ·
Biconditional :
" "
represented by >
ex if and only if & iff & P
.
p , p , >&
p is sufficient and necessary for
a
* TRUTH TABLES
Truth Table for Negation
P p
T F
F T
Truth Table for Pand a ,
por a or both ,
por a
,
p -
q ps q
p E P q p q pq p q P G
F F F F F T T
F T F T T T F
T F F T T F F
T T T T F T T
we don't want true
hypothesis testing something
that is false
examples
1 .
If it is sunny today ,
then we will go to the beach
F T =
T
.
2 If it is Friday today ,
then 2 + 3 =
5
F T = T
3
. If it is Friday today ,
then 2 + 3 = 6
F F =
T
/
.
4 Let s ,
+ ,
u denote the following statements :
s : Sam goes out for a walk
t: The moon is out
U : It is snowing
, Translate the following compound statements :
a( + u) S
·
If the moon is out and it is not snowing then Sam goes
out for a walk
b (s(n + )
·
It is not the case that Sam goes out for a walk if and
if it is snowing the is
only or moon out
C + (us)
·
If the moon is out ,
then if it isn't snowing (then)
Sam goes out for a walk
REVIEW :
·
negation >
- p p
TF
F T
·
truth tables :
P q pq P E pap q P q
T T T T F T T
T F F T T F F
F T F T T T F
F F F F F T T
* From example 4C make the truth table :
&
S t U U U S t ( us)
I
T T T T T
=
F T I T T
T T F T T
F T F T F F
T F T F T T
F F T F T T
T F F T T T
F F F T F T
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller jenniferolivetanojo. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for £7.71. You're not tied to anything after your purchase.
