Ct 100 week 3
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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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Ct 100 week 3

CT 100 Week 3

Logic


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)


And truth table

And Truth Table


Or truth table

OR Truth Table


Implies truth table

IMPLIES Truth Table


Equivalence truth table

Equivalence Truth Table


Not truth table

NOT Truth Table


Truth table for a and b or c

Truth Table for A AND (B OR C)


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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