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1 Chapter 2 Compound Statement A statement formed by joining two or more statements Conclusion In a conditional statement the statement that immediately follows the word then Conditional Statement a statement that can be written in the form “If p, then q.” p is the hypothesis and q is the conclusion. Symbolically, if p, then q can be written as p q. Conjunction a compound statement formed by joining two or more statements with the word “AND”. Conjecture A educated guess based on known information Converse In the converse of a conditional statement, the hypothesis and conclusion are reversed. “If p, then q.” becomes “If q, then p.”. 2 Chapter 2 Counterexample An example used to show that a given statement is not always true Deductive Reasoning A system of reasoning that uses facts, rules, definitions, or properties to reach logical conclusions Disjunction A compound statement formed by joining two or more statements with the word or Hypothesis In a conditional statement, the statement that immediately follows the word if If-then statement A compound statement of the form “If A, then B”, where A and B are statements Inverse The statement formed by negating both the hypothesis and conclusion of a conditional statement 3 Chapter 2 Law of Contrapositive in the contrapositive of a conditional statement, the hypothesis and conclusion are both reversed and negated. “If p, then q.” becomes “If not q, then not p.”. The contrapositive has the same truth value as the original statement. Law of Detachment If p→q is a true conditional and p is true, then q is also true Law of Syllogism If p→ q and q →r are true conditionals, then p→ r is also true Logically equivalent Statements that have the same truth value Negation Has opposite meaning Postulate postulate, or axiom, indicates a statement or assumption that is agreed by everyone to be so obvious or selfevident that no proof is necessary; and which can be used to prove other statements or theorems. Neither axioms nor postulates can be proved (within a system) using more basic statements. 4 Chapter 2 Proof a valid argument in which all of the premises are true Statement Any sentence that is either true or false, but not both Theorem a statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems Truth Table A table used as a convenient method for organizing the truth values of statements Truth Value The truth of falsity of a statement Two-Column Proof A formal proof that contains statements and reasons organized in two columns. Each step is called a statement, and the properties that justify each step are call reasons 5 Chapter 2 Venn Diagram show relationships between different sets of data. can represent conditional statements. It is usually drawn as a circle. Every point IN the circle belongs to that set. Every point OUT of the circle does not.