The document provides an overview of propositional logic including: 1. It defines statements, logical connectives, and truth tables. Logical connectives like negation, conjunction, disjunction and others are explained. 2. It discusses various logical concepts like tautology, contradiction, contingency, logical equivalence, and logical implications. 3. It outlines propositional logic rules and properties including commutative, associative, distributive, De Morgan's laws, identity law, idempotent law, and transitive rule. 4. It provides an example of using truth tables to test the validity of an argument about bachelors dying young.

1. PREPOSITIONal
LOGIC

2. A statement is a declaratory sentence which is true or
false but not both. In other words , a statement is a
declarative sentence which has a definate truth table.

3. Logical connectives or sentence
connectives
These are the words or symbols used to combine
two sentence to form a compound statement.
logic Name rank
~ Negation 1
^ Conjunction 2
V Disjunction 3
=> Conditional 4
 Biconditional 5

4. A B ^ V ~A =>  NOR NAND XOR EX-
NOR
T T T T F T T F F F T
T F F T F F F F T T F
F T F T T T F F T T F
F F F F T T T T T F T

5. TAUTOLOGY
i. A TAUTOLOGY IS A PREPOSITION WHICH IS
TRUE FOR ALL TRUTH VALUES OF ITS SUB-
PREPOSITIONS OR COMPONENTS.
ii. A TAUTOLOGY IS ALSO CALLED LOGICALLY
VALID OR LOGICALLY TRUE.
iii. ALL ENTRIES IN THE COLUMN OF
TAUTOLOGY ARE TRUE.

6. For example:
p^q=>q
P q p^q q p^q=>
q
T T T T T
T F F F T
F T F T T
F F F F T

7. Contradiction
 CONTRADICTION IS A PREPOSITION WHICH IS
ALWAYS FALSE FOR ALL TRUTH VALUES OF ITS
SUB-PREPOSITIONS OR COMPONENTS.
 A CONTRADICTION IS ALSO CALLED LOGICALLY
INVALID OR LOGICALLY FALSE
 ALL ENTRIES IN THE COLUMN OF
CONTRADICTION ARE FALSE.

8. FOR EXAMPLE
(P v Q)^(~P)^(~Q)
P Q PVQ ~P ~Q (P v Q)^(~P)^(~Q)
T T T F F F
T F T F T F
F T T T F F
F F F T T F

9. Contingency
It is a preposition which is either true or
false depending on the truth value of its
components or preposition..

10. FOR EXAMPLE
~p ^ ~q
p q ~p ~q ~p ^ ~q
T T F F F
T F F T F
F T T F F
F F T T T

11. Logical equivalence
Two statements are called logically equivalent if the truth
values of both the statements are always identical..
For example:
If we take two statements p=>q and ~q =>~p , then there
truth table values must be equal to satisfy the condition of
logical equivalence..

12. p q ~p ~q p=>q ~q=>~p
T T F F T T
T F F T F F
F T T F T T
F F T T T T
SINCE,THE TRUTH TABLE VALUES OF BOTH
STATEMENTS IS SAME. THUS, THE TWO
STATEMENTS ARE LOGICALLY EQUIVALENT..

13. LOGICAL IMPLICATIONS
 DIRECT IMPLICATION (p=>q)
 CONVERSE IMPLICATION (q=>p)
 INVERSE OR OPPOSITE IMPLICATION (~p=>~q)
 CONTRAPOSITIVE IMPLICATION (~q=>~p)

14. Algebra of
preposition
1) Commutative law
2) Associative law
3) Distributive law
4) De Morgan’s law
5) Idempotent law
6) Identity law

15. Idempotent law
1. pVpp
2. p^pp
p p pvp p v pp p^p p^ pp
T T T T T T
F F F F F F

16. Commutative law
• pvq=qvp
• p^q=q^p
p q pvq qvp p^q q^p
T T T T T T
T F T T F F
F T T T F F
F F F F F F

17. Associative law
• (p v q) v r  p v (q v r)
• (p ^ q) ^ r  p ^ (q ^ r)
p q r pvq ( p v q) v r qVr p v (q v r)
T T T T T T T
T T F T T T T
T F T T T T T
T F F T T F T
F T T T T T T
F T F T T T T
F F T F T T T
F F F F F F F

18. Distributive law
• p ^ (q v r)  (p ^ q) v (p ^ r)
• p ^ (q v r)  (p ^ q) v (p ^ r)
p q r qvr p^(q v r) p^q p^r (p^q)v(p^r)
T T T T T T T T
T T F T T T F T
T F T T T F T T
T F F F F F F F
F T T T F F F F
F T F T F F F F
F F T T F F F F
F F F F F F F F

19. De Morgan’s law
• ~(p v q)  ~p ^ ~q
• ~(p ^ q)  ~p v ~q
p q (p v q) ~(p v q) ~p ~q ~p ^ ~q
T T T F F F F
T F T F F T F
F T T F T F F
F F F T T T T

20. Identity law
1) p ^ T  p 2) T ^ p  p
3) p v F  p 4) F v p  p
P T P^T P F P v F
T T T T F T
F T F F F F

21. TRANSITIVE RULE
pq
qr
--------------
pr
Rule of detachment
P
Pq
----------
q

22. EXAMPLE
TEST THE VALIDITY OF THE FOLLOWING
ARGUMENT….
IF A MAN IS A BACHELOR,HE IS WORRIED(A PREMISE)
IF A MAN IS WORRIED,HE DIES YOUNG(A PREMISE)
-----------------------------------------------------------------------------------------------------
BACHELORS DIE YOUNG(CONCLUSION)
P: A man is a bachelor
Q:he is worried
R: he dies young

23. The given argument in symbolic form can be
written as:
pq (a premise)
qr (a premise)
--------------------
pr (conclusion)
The given argument is true by law of
syllogism(law of transitive)…

24. p q r pq qr pr pq ^ qr (pq) ^ (qr)
=> pr
T T T T T T T T
T T F T F F F T
T F T F T T F T
T F F F T F F T
F T T T T T T T
F T F T F T F T
F F T T T T T T
F F F T T T T T

25. PRESENTATION BY :
ASHWINI VIPAT