propositions

• Logical connectives


  Symbols, words used to combine propositions
• 1+1=1, 1+0=0
• Conditional


  If then
• At least 1=1
• Biconditional


  If and only if
• Both T/F=1
• Proposition


  Statements that can be either true or false
• Types of propositions


  • Atomic proposition
  • Compound proposition
• Atomic proposition


  Statement that's either true or false and denoted by variables (p,q,r). Single statement, indivisible.
• Compound proposition


  Combination of one or more atomic propositions with the help of connectives
• Conditional statement (implication) can also be denoted as ⇒
• Number of rows in a truth table is 2^n, where n is the number of variables
• Rows in a truth table represent all possible combinations of true and false values
• A disjunctive proposition presents alternatives, indicating that at least one of the options is true.

  
• A hypothetical proposition expresses a conditional relationship, typically using an "if-then" structure.
• A proposition is an expression that can be true or false
• The truth value of a proposition depends on the world it's evaluated in
• Propositional logic deals with statements, not objects
• Propositional logic deals with propositions, their truth values, and how they relate to one another
• The negation operator changes the value of a proposition from true to false or vice versa.
• Disjunction represents an inclusive OR operation, meaning both options may be true simultaneously.
• Conjunction combines two or more statements into a single compound proposition.
• The negation operator changes the truth value of a proposition from true to false or vice versa.
• An existential proposition affirms the existence of something, often expressed through quantifiers such as "there exists."
• The negation of a proposition is formed by adding the word 'not' to it
• A universal proposition makes a general claim about everything within its scope, usually indicated by phrases like "for all" or "everything."
• We can combine these symbols into more complex expressions called formulas
• Formulas are built up from atomic propositions by applying logical connectives like conjunction (∧), disjunction (∨), negation (¬)
• We use connectives to combine propositions into more complex expressions
• Conditional (→) represents a material implication between two propositions, where if the first proposition is true then the second proposition must also be true.
• Disjunction (∨) combines two propositions into a single compound proposition whose truth value is determined by at least one component proposition being true.
• Conjunction (∧) combines two propositions into a single compound proposition whose truth value is determined by both component propositions being true.
• Connectives are used to create new propositions from existing ones
• In propositional logic, we use symbols (propositional variables) to represent propositions
• Compound propositions are formed by combining simpler propositions with logical connectives such as conjunction (∧), disjunction (∨), negation (¬)
• In propositional logic, we use symbols to stand for propositions
• Implication represents a conditional statement, where if the first condition is true, then the second condition must also be true.
• Conditional is used when there are two propositions that have some sort of relationship between them.
• Conjunction represents an AND operation, where all conditions must be met for the statement to be true.
• Equivalence represents two expressions being equivalent, meaning they have the same truth value.