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# CT 100 Week 3 - PowerPoint PPT Presentation

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

Logic

• Vocabulary from week 1 and 2

• Conclusion

• Law of excluded middle

• Boolean Logic

• Premise

• Proposition

• Syllogism

• Symbolic logic

• Tautology

• Truth table

• Definitions for the new terms are at the end of chapter 3

• 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

• 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

• Querying a relational database

• Digital logic

• Software development

• The study of the principles of valid inferences

• The science of correct thinking

• Inductive logic

• Deductive logic

• All men are mortal

• Aristotle is a man

• Aristotle is mortal

• 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?

• 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

• 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?

• All elements of set A have property B

• C is an element of set A

• C has property B

• All elements of set A have property B

• C does not have property B

• C is not an element of set A

• Proposition

• A statement that is either true of false

• Logical connectives

• AND (Conjunction)

• OR (Disjunction)

• NOT (Negation)

• IMPLIES (Implication)

• ≡ (Equivalence)

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)

• 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

• 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