Mathematical Thinking Stanford, W3 Assignment 5
(∀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 $q=1$)] ...