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Discrete Structures

Exam 1

QuestionAnswer
Statement/Proposition A sentence that’s T/1 or F/0 - ABC: Letters that represents Statements - Ex: There are life forms in some planets. - Not 'He is tall' since we don’t know who is ‘he’
Logical Operator: || Takes the maximum value of A & B | Only 1 False - Ex: A ∨ B - Eng Words: And, but, also, more over
Logical Operator: && Takes the minimum value of A & B | Only 1 True - Ex: A ^ B - Eng Words: And, but, also, more over
Logical Operator: Negation` Opp. of A - Eng Words: It’s false that A
Logical Operator: Implication (→) A → B | Only false when A is true & B is false - Eng Words: If A, then B | A implies B | A only if B
Logical Operator: Equivalence ←→ | Only true when A & B are the same values - Eng Words: A if & only if B | A is necessary & sufficient for B
Order/ Precedence for Logical Connectives 1. Innermost Parentheses 2. ` 3. ∨, ∧ 4. → 5. ←→
Well-Formed Formulas (wff) An expression that’s a legitimate string - PQRS: Letters to represent wff - Practice by Chapter 1.1 Exercise 1 (A - D)
Tautology vs Contradiction wff Tautology: A wff that’s always true = 1 - Ex: A ∨ A` Contradiction: A wff that’s always false = 0 - Ex: A ∧ A`
Equivalent wff P ←→ Q = (P → Q) ∧ (Q → P) - Ex: If P ←→ Q are both wff & a tautology, P can replace Q & vice versa
Determining T/F Combos for N Expressions Use 2^N
Properties: Identity - A v 0 = A - A ^ 1 = A
Created by: Whateverisfree
 

 



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