Algorithm, Information Logic

							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

KONTRADIKSI:
 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

Ershad Khaliva