MMW CHAP 3

• Gottfried Wilhelm Leibniz - one of the first mathematicians to seriously study symbolic logic.
• Augustus De Morgan and George Boole - contributed to advancing symbolic logic as a mathematical discipline.
• A statement or proposition is a declarative sentence that is either true or false, but not both simultaneously.
• A simple statement is a statement that conveys a single idea.
• A compound statement is a statement that conveys two or more ideas.
• The truth (T) or falsity (F) of a proposition is called truth value
• A table that summarizes truth values of propositions is called a truth table.
• Mathematician George Boole used symbols such as p,q,r and s to represent symbols.
• The denial of a statement is called its negation
• Quantifiers are symbols used to express the extent of generality of a statement.
• If p and q denote two propositions, the compound proposition "p and q" is called the conjunction of p and q
• A compound proposition formed by joining two or more propositions by the word "or" is called disjunction.
• The proposition "if p, then q" is called a conditional or an implication.
• Proposition p is called the antecedent or hypothesis
• Proposition q is called the consequent or conclusion.
• The conditional statement and its contrapositive always have the same truth values, as do the converse and the inverse
• Biconditional is a logical connective used in mathematical logic to express a bidirectional relationship between two statements.
• The word biconditional means "two conditionals"
• Parentheses are used to indicate which simple statements are grouped whenever a compound statement is expressed in symbolic form.
• The comma is used to indicate which simple statements are grouped.
• Two statements are said to be equivalent if they both have the same truth value for all the possible truth values of their simple statements.
• An argument consists of a set of statement called premises and another statement called the conclusion.
• An argument is valid if the conclusion is true whenever all the premises are assumed to be true.
• An inductive argument uses a collection of specific examples as its premises and uses them to propose a general conclusion. ( from specific to general)
• A deductive argument uses a collection of general statements as its premises and uses them to propose a specific situation as the conclusion (from general to specific)
• It is a diagram consisting of various overlapping figures contained within a rectangle (called the universe)
• Modus ponens (the mode of affirming)
• Modus tollens (the mode of denying)
• Fallacy of the converse (fallacy of affirming the conclusion)
• Fallacy of the inverse (fallacy of denying the hypothesis)