Prepositional Logic

Prepositional Logic 

Definition : A proposition or statement is a sentence which is either true or false If a proposition is true, then we say its truth value is true, and if a proposition is false, we say its truth value is false.

Example : 

1. The sun is shining. (True)

2. The sum of two prime numbers is even. (False)

3. 3+4=7 (True)

4. It rained in Austin, TX, on October 30, 1999. (False)

5. x+y > 10 (True)

6. n is a prime number. (True)

7. The moon is made of green cheese. (False)

Prepositional Variables 

Definition : A propositional variable represents an arbitrary proposition. We represent propositional variables with uppercase letters.

Example : We use letters P, Q, R, S, to denote propositional variables.

we may use the letter P to refer to “All penguins are birds” and the letter S for “Socrates is mortal”. We can then perform logical operations on these words, and say something like P ∧ S, or “All penguins are birds, and  Socrates is mortal.”

Types of truth tables 

1.     Negation

~	P
F	T
T	F

2.    Conjunction

P	.	q
T	T	T
T	F	F
F	F	T
F	F	F

3.    Disjunction

P	V	q
T	T	T
T	T	F
F	T	T
F	F	F

4.    Material Equivalence

P	Ξ	q
T	T	T
T	F	F
F	F	T
F	T	F

5.    Material Implication

P	É	q
T	T	T
T	F	F
F	T	T
F	T	F