Propositional logic involves analyzing statements called propositions that can be either true or false. Propositions are combined using logical connectives like "and", "or", and "if/then" to form compound statements. A tautology is a statement that is always true no matter the truth values of the individual propositions. A contradiction is always false, while a contingency can be either true or false depending on the propositions. Two statements are logically equivalent if they have identical truth tables.

1. PROPOSITIONAL LOGIC
PRESENTED BY : CRAZY ENGINEERS

2. ABDULLAH AL AMIN
ID: 171 – 15 - 9365

3. WHAT IS PROPOSITION ?
Statement
Declaratory
FalseTrue

4. EXAMPLE OF PROPOSITION
 We give a statement that
 Dhaka is the capital of Bangladesh
 This statement or sentence is a proposition because of two reason
Declarative
Has truth
value

5. LOGICAL CONNECTIVES
There are some word 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

6. BASIC LOGICAL OPERATIONS
A B ^ V ~ A => ↔ NOR NAN
D
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

7. MD TOUHIDUL ISLAM SHAWAN
ID: 171 – 15 – 9354

8. TAUTOLOGY
Statement
PropositionTrue

9. EXAMPLE OF TAUTOLOGY
We have a statement that “ I will get in trouble or not get in trouble “ .
Proposition p = I will get in trouble.
p ⌐ p p ᴠ ⌐ p
T F T
F T T

10. MD NOUSHAD ALI
ID: 171 – 15 – 9349

11. CONTRADICTION
Contradiction
Proposition False

12. TRUTH TABLE
P Q P ᴠ Q ~ 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

13. SHAKAWAT HOSSEN
ID: 171 – 15 - 9346

14. CONTINGENCY
Contingency
NeitherTautology Contradiction

15. TRUTH TABLE
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

16. AKASH CHANDRA DAS
ID: 171 – 15 – 9351

17. LOGICAL EQUIVALENCE
P
Q
Logically
Equivalent
P ↔Q is tautology

18. EXAMPLE
If we take statements p => q and ~ q => ~p, then there truth table values must be
equal to satisfy the condition of logical equivalence
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