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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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CT 100 Week 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


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