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# burton_discrete_logic

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### Transcript

• 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.