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CT 100 Week 3

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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  1. CT 100 Week 3 Logic

  2. 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

  3. 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

  4. 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

  5. Applications • Querying a relational database • Digital logic • Software development

  6. Logic • The study of the principles of valid inferences • The science of correct thinking • Inductive logic • Deductive logic

  7. Deduction • All men are mortal • Aristotle is a man • Aristotle is mortal

  8. 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?

  9. 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

  10. 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?

  11. Deduction • All elements of set A have property B • C is an element of set A • C has property B

  12. Deduction • All elements of set A have property B • C does not have property B • C is not an element of set A

  13. Boolean Logic • Proposition • A statement that is either true of false • Logical connectives • AND (Conjunction) • OR (Disjunction) • NOT (Negation) • IMPLIES (Implication) • ≡ (Equivalence)

  14. And Truth Table

  15. OR Truth Table

  16. IMPLIES Truth Table

  17. Equivalence Truth Table

  18. NOT Truth Table

  19. Truth Table for A AND (B OR C)

  20. 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)

  21. 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

  22. 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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