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burton_discrete_logic

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  • 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.

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