Algorithm, Information Logic

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Algorithm, Information Logic

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```							Information Logic

Yudy P
NATURE OF SENTENCE LOGIC

VALID :
A sentence f is called valid, if for every iterpretation I for f, then f
true
Example:
a. (f and q) if and only if (q and f)
b. f or not f
c. (p and (if r then s)) if and only if (if r then s) and p)
d. (p or q) or not (p or q)
e. (if p then not q) if and only if not (p and q)
NATURE OF SENTENCE LOGIC

SATISFIABLE:
 A sentence f is called satisfiable, if for the interpretation I for f,
then the true
Example:
a. if (if p then q) then q
b. (if p then q) or (r and s)
c. (if p then q) or r
NATURE OF SENTENCE LOGIC

 A sentence is called contradiction f, if for every interpretation I for
f, then f false

example:
a. p and not p
b. ((p or q) and not r)) if and only if ((if p then r) and (if q then r))
SENTENCE BERKUANTOR

Statement containing the expression quantity of objects involved,
Eg all, any, some, not all etc..

There are two kinds kuantor :
1. Universal Quantifier ( for all …)
Have a general and comprehensive meaning
notation: , read all, all, every
writing : x  S  p(x)
” All the x in the universe s have the property p”

Example:
- All who live must die
- every student must be clever
- all students Harvard handsome and beautiful
2. Existential Quantifier ( for some …)
Have a special meaning or partially
Notation : , read there, there, some
Writing: y S  q(y)
"There s y in the universe has the properties of q"
Example:
There are students in this class are sleepy.
Some students who got an A course Logic and Algorithms
SENTENCE INGKARAN
BERKUANTOR

1. If the sentence contains kuantor uinversal then ingkarannya be
kuantor existential and nature at deny.
~ (( x) p (x)) = ( y) (~ p (y))

Example:
p: all Harvard students should tie
~ p: There is a Harvard student who does not tie

2If the sentence contains an existential kuantor kuantor then
ingkarannya become universal and are in deny.
~((y) q(y)) = (x) (~q(x))

Example:
q: There is acting that corruption
~ p: All the officials are not corrupt
Conclusion Based on the
Implications

Modus Ponens:
Pq
P
q
Example:
If a student then it is definitely good at it
Tamar is a student
 Tamara definitely clever
Conclusion Based on the
Implications

Modus Tellens:
Pq
~q
~p

Example:
If inul is a good student so he would not cheat in exams
Inul cheat in exams
inul not a good student
Conclusion Based on the
Implications

Prinsip Syllogisme:
pq
qr
pr

Example:
If he is diligent he is definitely smarter
If he was smart then he must be successful
** if he is diligent and he must be successful
Conclusion Based on the
Implications

Examples of other Prinsip Syllogisme :

A = You study diligently
B = You pass
C = You are happy

Argument result:
AB
BC
---------
AC
Conclusion Based on the
Implications

Dilemation
p v q
pr
qr

r
example :
He's gone or he's back
If he goes then we are losing
If he comes back then we are losing
**We will lose
QUIZ

1. What is a declarative sentence?, what is the relationship with nature
sentence logic and give example sentences loginya.
2. Prove that the following sentence Valid properties.
(p and (if q then r)) if and only if ((if q then r) and p)
3. Determine the truth value of sentence following logic using the truth
table:
1. (f and g) if and only if (not (g and g))
2. if (if p then q) then q
3. ((p or q) and not r) if and only if ((if p then r) and (if q then r))
4. ((if p then q) and (if q then p)) if and only if (not q or not p)
5. (p and (if s then r)) if and only if ((if r then s) and p))
4. Give an interpretation for each constituent proposition that sentence
The following logic is false if (p and q) then (r or s)
5. Know of a logical sentence as follows:
(if (p and q) then (if r then s)) if and only if (if p then (q or not r) or s))
a. Determine the truth value of the sentence if p = true, q = false, r = true
and s = true.
b. Define an interpretation so that the sentence is false.
QUIZ

From this sentence the following sentence, determine the truth
value by using the truth table:
a. If ((if q then p) or not q) then ((p if and only if q)) else note r))
b. If (if p then (if q then r)) then ((if p then q else (not (if r then
q)))
c. If given two implications as follows:
If ((p or q) or (not (p or q)) then ((f and g) if and only if (g and f))
If ((f and g) if and only if (g and f)) then (p and not p)
Determine conclusions by using the principle
Syllogisme, and give its truth value by using truth tables.
Thanks

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