Quantifier(logic) $∀$ , For All, Conjunction, ∧, all things $∃$, Exist, Disjunction, ∨, at least one $∃x$[$A(x) ∧ B(x)$] ≠ $∃x$$A(x)$ ∧ $∃x$$B(x)$, False There is a game player who is both an attacker and a defender. There is a game player who is an attacker, and There is a game player(another one?) who is a defender. $∃x$[$A(x) ∨ B(x)$] = $∃x$$A(x)$ ∨ $∃x$$B(x)$ There is a game player who is an attacker or a defender. ...

(∀𝑚∈ ℕ)(∃𝑛 ∈ ℕ)(𝑛>𝑚), True Express the existence assertions a. ($∃x$ ∈ ℕ)($x^3 = 27$ ) b. ($∃𝑛$ ∈ ℕ)(𝑛>10000) c. natural number n is not a prime ($∃p$ ∈ ℕ)($∃m$ ∈ ℕ)($p$>1 ∧ $m$>1 ∧ $n=pm$) Express the ‘for all’ assertions a. ($∀x$ ∉ ℕ)($x^3$ = 28) ¬($∃x$ ∈ $ℕ$)($x^3$ = 28) ($∀x$ ∈ ℕ)($x^3$ ≠ 28) ($∀x$ ∈ ℕ)¬($x^3$ = 28) b. ($∀n$ ∈ ℕ)($n>0$ ) c. ($∀p$ ∈ ℕ)($∀q$ ∈ ℕ)[( $n=pq$) ⇒ ($p=1$ V $q=1$)] ...

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 ? ...