Propositional logic Irina Prosvirnina
Propositions
Propositions
Propositions
Propositions
Propositions
Compound propositions
Compound propositions
The negation of a proposition
The negation of a proposition
The negation of a proposition
The conjunction of two propositions
The conjunction of two propositions
The conjunction of two propositions
The conjunction of two propositions
The disjunction of two propositions
The disjunction of two propositions
The disjunction of two propositions
The disjunction of two propositions
The exclusive or
The exclusive or
The exclusive or
The exclusive or
Conditional statements
Conditional statements
Conditional statements
Conditional statements
Conditional statements
Converse, contrapositive and inverse
Converse, contrapositive and inverse
Biconditionals
Biconditionals
Biconditionals
Biconditionals
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Truth tables of compound propositions
Precedence of logical operators
Precedence of logical operators
Precedence of logical operators
Precedence of logical operators
Precedence of logical operators
Tautologies and contradictions
Tautologies and contradictions
Tautologies and contradictions
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
Logical equivalences
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
A Demonstration That p(qr) and (pq)(pr) Are Logically Equivalent.
Logical equivalences
Logical equivalences
Logical equivalences
Using De Morgan’s Laws
Using De Morgan’s Laws
Constructing new logical equivalences
Constructing new logical equivalences
Constructing new logical equivalences
Constructing new logical equivalences
Constructing new logical equivalences
Constructing new logical equivalences
Constructing new logical equivalences
Propositional satisfiability
Propositional satisfiability
Propositional satisfiability
Propositional satisfiability
Propositional satisfiability
Satisfiability problem
Sudoku 99
Sudoku 99
Sudoku 99
2.70M
Категория: МатематикаМатематика

Propositional logic

1. Propositional logic Irina Prosvirnina

• Propositions
• Compound propositions
• Conditional statements
• Truth tables of compound propositions
• Tautologies and contradictions
• Logical equivalences
• Propositional satisfiability
• Satisfiability problem

2. Propositions

Our discussion begins with an introduction to the basic
building blocks of logic – propositions.
Definition 1
A proposition is a declarative sentence (that is, a
sentence that declares a fact) that is either true or
false, but not both.

3. Propositions

Example 1
All the following declarative sentences are propositions.
1. Minsk is the capital of Belarus.
2. Toronto is the capital of Canada.
3. 1+1=2.
4. 2+2=3.
Propositions 1 and 3 are true, whereas 2 and 4 are false.

4. Propositions

Example 2 Consider the following sentences.
1. What time is it?
2. Read this carefully.
3.
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