3. Definition :
A proposition is a declarative sentence that is either
TRUE or FALSE, but NOT BOT
The example of declarative sentence that are not propositions:
1. Zulhelmy will not win the Thomas cup this year.
x+1=3
2. Kuala Lumpur is a capital of Malaysia.
2+2=4
4.
5. Notation
We use letters to denote propositional variables that represent
propositions.
The conventional letters used to denote numerical variable.
The conventional letters used for propositional variables are p ,
q , r , s ,…..
The area of logic that deals with propositions is called
propositional calculus or propositional logic.
9. 1. Propositional Logic –
Negation
Negation is an other propositions
The compound proposition is “it is not the case that p”.
It called the negation of p and the denoted of ⌐p .
The truth value of the negation of p is the opposite of the
truth value of p. The proposition ⌐p is also can say as “not
p”.
10.
11. Example 1
Example :
Discrete mathematics is Hasrul’s favorite subject. ( p )
Discrete mathematics is NOT Hasrul’s favorite subject.(⌐p )
Truth the table for negation :
p ⌐p
True False
False True
The truth table presents the relations between the truth values
of many propositions involved in a compound proposition
12.
13. 2. Propositional Logic –
Conjunction
Conjunction is a compound proposition that has
components joined by the word and or its symbol.
It is true only if both or all the components are true.
Let p and q be propositions :
The compound proposition “p and q“ .
“p ˄ q”, is true when both p and q are true and
false otherwise
14.
15. Example 2
Example :
Faiz is a singer (p) and dancer (q).
Truth the table for conjunction :
p q p˄q
T T T
T F F
F T F
F F F
16.
17. 3. Propositional Logic –
Disjunction
Disjunction is a proposition that presents two or more
alternative terms, with the assertion that only one is true.
The compound proposition “p or q“ or “p ˄ q“, is false
when both p and q are false and true otherwise.
The compound proposition “p ˄ q“ is called disjunction
of p and q.
18.
19. Example 3
Example :
Faiz is a singer (p) or dancer (q).
Truth the table for disjunction:
P Q p˄q
T T T
T F T
F T T
F F F
20.
21. 4. Propositional Logic –
Exclusive Disjunction
Exclusive Disjunction is a Logic the connective.
It gives the value true to a disjunction if one or other, but
not both, of the disjunction are true.
The compound proposition “p exclusive or q“, denoted
“p ⊕ q“, is true when exactly one of p and q is true and
is false otherwise.
This compound proposition “p ⊕ q“ is called exclusive
disjunction of p and q.
22.
23. Example 4
Example :
You can have a PS2 (p) or PSP (q).
Truth the table for the exclusive disjunction:
p q p⊕q
T T F
T F T
F T T
F F F
