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CT 100 Week 3. Logic. Week 3 Vocabulary. Vocabulary from week 1 and 2 Contradiction Conclusion Law of excluded middle Law of non-contradiction Boolean Logic Premise. Proposition Syllogism Symbolic logic Tautology Truth table Definitions for the new terms are at the end of chapter 3.

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week 3 vocabulary
Week 3 Vocabulary
  • Vocabulary from week 1 and 2
  • Contradiction
  • Conclusion
  • Law of excluded middle
  • Law of non-contradiction
  • Boolean Logic
  • Premise
  • Proposition
  • Syllogism
  • Symbolic logic
  • Tautology
  • Truth table
  • Definitions for the new terms are at the end of chapter 3
week 3 quiz problems
Week 3 Quiz Problems
  • Convert binary to base 10
  • Convert base 10 to binary
  • Convert a sequence of characters to a sequence ASCII codes (numbers)
  • Convert a sequence of numbers representing characters in ASCII to a sequence of characters
  • Create a truth table for a boolean expression
logic problems
Logic Problems
  • Create a truth table for a logical expression
  • Determine if a proposition is a tautology
  • Determine if a proposition is a contradiction
  • Translate a proposition written in English into a proposition written in symbolic logic
  • Determine if an expression is a well-formed proposition
applications
Applications
  • Querying a relational database
  • Digital logic
  • Software development
logic
Logic
  • The study of the principles of valid inferences
  • The science of correct thinking
  • Inductive logic
  • Deductive logic
deduction
Deduction
  • All men are mortal
  • Aristotle is a man
  • Aristotle is mortal
deduction1
Deduction
  • Items 1 and 2 are called premises
  • Item 3 is called a conclusion
  • Is the conclusion valid?
  • Is the conclusion (Aristotle is mortal) a valid inference or valid conclusion of premises 1 (All men are mortal) 2 (Aristotle is a man)?
  • Is the conclusion true?
deduction2
Deduction
  • Every tove is slithy*
  • Alice is not slithy
  • Alice is not a tove

* From A Course in Mathematical Logic by John Bell and Moshe Machover

deduction3
Deduction
  • Is the conclusion (Alice is not a tove) a valid inference of premise 1 (Every tove is slithy) and premise 2 (Alice is is not slithy )?
  • Is the conclusion true?
deduction4
Deduction
  • All elements of set A have property B
  • C is an element of set A
  • C has property B
deduction5
Deduction
  • All elements of set A have property B
  • C does not have property B
  • C is not an element of set A
boolean logic
Boolean Logic
  • Proposition
    • A statement that is either true of false
  • Logical connectives
    • AND (Conjunction)
    • OR (Disjunction)
    • NOT (Negation)
    • IMPLIES (Implication)
    • ≡ (Equivalence)
true table practice problems show the truth table for the following boolean expressions
True Table Practice ProblemsShow the truth table for the following Boolean Expressions
  • A AND B
  • A AND (NOT B)
  • (NOT A) AND B
  • NOT (A AND B)
  • (A OR B) AND (C OR D)
  • NOT (A OR B)
  • A IMPLIES B
  • (NOT B) IMPLIES (NOT A)
  • NOT (A IMPLIES B)
  • A ≡≡ B
  • NOT (A ≡ B)
  • A OR (NOT A)
  • A AND (NOT A)
  • NOT (A IMPLIES (NOT B))
  • ((A IMPLIES B) AND ( B IMPLIES A)
  • A IMPLIES (B IMPLIES A)
translating english to symbolic logic
Translating English to Symbolic Logic
  • The English language statements must be propositions (i.e. statements that are either true or false)
  • Example simple statements
    • Sue was born in Wisconsin
    • It rained on Sunday
    • Mike was born in 1993
    • I am not thirsty
translating english to symbolic logic1
Translating English to Symbolic Logic
  • Example compound statements
    • Mary was born in Minnesota and Mary was born in 1992
      • Mary was born in 1992 in Minnesota
    • Mary was not born in Minnesota
    • Sam was born in neither Wisconsin nor Ohio
    • If it is raining then I will open my umbrella
    • If I study then I will pass ct 100
    • I will pass ct 100 only if I study