Internet

the most difficult lecture Analysis of language - quantifiers irrational numbers ∀ for all ∃ there exists express an existence assertion. a confident and forceful statement of fact or belief. Combination of quantifiers there is no largest natural number. (∀𝑚∈ ℕ)(∃𝑛 ∈ ℕ)(𝑛>𝑚), True (∃𝑛 ∈ ℕ)(∀𝑚∈ ℕ)(𝑛>𝑚), False American Melanoma Foundation: “One American dies of Melanoma almost every hour.” ∃A∀H(A dies in hour H), False, misunderstanding: An American dies once every hour, ridiculous. ...

1. Building truth table φ ⇔ ψ φ ψ φ ⇒ ψ ψ ⇒ φ φ ⇔ ψ T T T T ✔︎ T F F T F T T F F F T T ✔︎ a. φ ⇔ ψ is true if φ and ψ are both true or both false (φ ⇒ ψ)=(ψ ⇒ φ) , (φ ⇒ ψ)∧(ψ ⇒ φ) = φ ⇔ ψ, φ = ψ ...

Math Foundation of computing, Stanford university. Preliminary Course Notes - Keith Schwarz implication has a truth part(conditional) and a causation part. implication = conditional + causation conditional means ⇒ φ ⇒ ψ is the truth part of “ φ implies ψ ”. φ is the antecedent ψ is the consequent define the truth of φ⇒ψ in terms of the truth/falsity of φ and ψ. Equivalence Quiz Which of the following conditions is necessary and sufficient for the natural number $n$ to be multiple of 10 ? ...

1. D, Y, T a. T ⇒ [D ∧ Y] b. D ⇒ ¬ Y c. ¬ D ⇒ ¬ T d. T ⇒ ¬ (D ∧ Y) e. ¬ D ∧ Y ∧ T , T ⇒ [¬ D ∧ Y], following means “then or and”, they are all conjunctions relationship. f. (T ∧ Y) ⇒ ¬ D , T ⇒ [Y ⇒ ¬ D] g. T ⇒ [D ⇔ Y], T⇒ [(D ⇒Y) ∧ (Y⇒D)] ...

1. Simplify the symbolic statements. (b) (p≥7)∧(p<12), 7≤p<12 (c) (x>5)∧(x<7), 5<x<7 (d) (x<4)∧(x<6), x<4 (e) $(y<4)∧(y^2 <9), y^2<9$ (f) (x≥0)∧(x≤0), x=0 2. Express each of your simplified statements from question 1 in natural English. (b) p is greater than or equal to 7 and less than 12. (c) x is greater than 5, and less than 7. (d) x is less than 4 (e) y squared is less than 9 (f) x is equal to 0 ...