Inductive reasoning uses patterns while deductive reasoning uses facts. Logical statements can be true or false. Simple statements contain one idea while compound statements contain several ideas. Connectives like "and", "or", and "if...then" are used to join the ideas in compound statements. There are five basic connectives: negation, conjunction, disjunction, conditional, and biconditional. Quantifiers include universal and existential words. Truth tables are used to determine if statements are tautologies or always true based on the combinations of true and false for each component. Arguments contain premises that lead to a conclusion, and are valid if the premises are true.

1. Compiled By: Ni-Ni Seth Dominique Brittany Keshawn LOGIC

2. Inductive and Deductive Reasoning Inductive reasoning- is using patterns. Deductive reasoning-is using facts.

3. Logical sentence that is true or false. Represent statements w/ lowercase letters. Simple statement- contains 1 ideal Compound statement- contains several ideas. Statements are....

4. Are used to join the ideas of a compound system. Examples: And, Or, But, If then, and if and only if. Connectives

5. Negation-express that something is not true. Conjunction-idea of and. Disjunction- idea of Or Conditional- idea of if…then. Biconditional-idea of if and only if. 5 Connectives

6. Universal-words such as all and every. Existential-words such as some, there exsits, and there is at least one. Quantifiers

7. Negation: ~ Conjunction: ^ Disjunction: v Quantifier Symbols

8. B: The blue whale is the largest living creature. ~B: The blue whale is not the largest living creature. Negating Statements

9. Negation- reverses the truth Conjunction-both parts are true. Disjunction- false when both are false. Tautology- statement always true. Truth Tables

10. Conjunction a Statement P: the tenant pays utilities D: $150 deposit is required p^d: the tenant does not pay utilities and a $150 deposit it is required ~( p^d): It is not true…

11. Conditional and Biconditional Conditional-is false when T then F. Biconditional-true when the components are both T or both F

12. Conditional p  q Converse: If q  p Inverse: ~p  ~q Contrapositive: ~q  ~p

13. Argument - a series of statements called Premises followed by a single statement called a conclusion. An argument is valid when all premises are true. Verifying Arguments

14. Practice Problems If it rains tomorrow, then I will bring an umbrella. Find the Converse, Inverse, and the Contrapositive.

15. Practice Problems Cont… R: the playground is wet. S: the playground is cold. Using the statement above make it a conjunction, disjunction, conditional, and a Biconditional.