Principles of text to predicate logic

Some are F          ∃ x. F(x)

Some F are G        ∃ x. F(x) ∧ G(x)
 *a. ∃ x. F(x) ∧ G(x)
  c. ∃ x. F(x) → G(x)
  d. ∃ x. G(x) → F(x)
  b. ∃ x. F(x) ∨ G(x)
  e. ∃ x. F(x) ←→ G(x)


All are F           ∀ x. F(x)

All F are G         ∀ x. F(x) → G(x)
  a. ∀ x. F(x) ∧ G(x)
 *c. ∀ x. F(x) → G(x)
  b. ∀ x. F(x) ∨ G(x)
  d. ∀ x. G(x) → F(x)
  e. ∀ x. F(x) ←→ G(x)

All two-digit primes are odd
    F(x): x is a two-digit prime
    G(x): x is odd
    ∀ x. F(x) → G(x)


None are F          ∄ x. F(x)

No F is G               F = is a fiend   G = is good
 *a. ∀ x. ¬F(x) ∨ ¬G(x)
 *b. ∀ x. F(x) → ¬G(x)
 *c. ∄ x. F(x) ∧ G(x)
  d. ∄ x. F(x) → G(x)
  e. ∀ x. F(x) xor G(x)
  
∀ x. ¬F(x) ∨ ¬G(x)
∀ x. ¬(F(x) ∧ G(x))
¬∃ x. (F(x) ∧ G(x))
∄ x. F(x) ∧ G(x)