MMW CHAPT 3

• Gottfried Wilhelm Leibniz (1646-1716) was one of the first mathematicians to seriously study symbolic logic
• A statement or proposition is a declarative sentence that is either true or false but not both simultaneously
• Negation is the denial of a statement, denoted as ~p and called "not p"
• Quantifiers are symbols used to express the extent of generality of a statement, crucial in formalizing statements and defining variables in logical formulas
• Conjunction, denoted as "p and q," is true only if both p and q are true, otherwise it's false
• Disjunction, denoted as "p or q," uses the word "or" in the inclusive sense
• Implication: proposition p is the antecedent or hypothesis, and q is the consequent or conclusion
• Converse is formed by interchanging the hypothesis with the conclusion
• Inverse is formed by negating the hypothesis and negating the conclusion
• Contrapositive is formed by negating both the hypothesis and the conclusion and interchanging these negated statements
• Biconditional is a logical connectivity used in mathematical logic to express a bidirectional relationship between two statements
• Compound statements in mathematical logic involve combining simple statements using logical connectives to form more complex statements
• Parentheses are used to group compound statements, while commas indicate grouped simple statements
• An argument consists of sets of statements named premises and a conclusion; the argument is valid if all the premises are true
• Types of arguments:

  • Inductive: uses specific examples to propose a general conclusion
  • Deductive: applies to a specific situation as the conclusion
• Standard forms of valid argument: rules of inference are methods used to draw valid conclusions from premises in deductive reasoning