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CT 100 Week 3

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CT 100 Week 3

Logic

- 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

- 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)

- 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

- Mary was born in Minnesota and Mary was born in 1992