Tychonievich is a professor A Sherriff is a professor B Sullivan is a professor C Skadron is a professor D Horton is a professor Dwyer is a professor Xu is a professor ________ is a professor -- predicate Tychonievich is a professor Tychonievich is a baker Tychonievich is a artist Tychonievich is a poet Tychonievich is a _________ _________ is a _________ P(x, y) === _______x is a ______y P(Tychonievich, Poet) B(x, y) === x ←→ y At least one number is prime Universe of Discourse is numbers P(x) === _____x is prime ∃ x . P(x) ∃ x . !!P(x) !∀ x . !P(x) It is not the case that all numbers are not prime N(x) === _____x is a number P(x) === _____x is prime Universe of Discourse is stuff ∃ x . N(x) ^ P(x) ∃ x . N(x) → P(x) WRONG x is Tommy ∃ x . N(x) ←→ P(x) WRONG second in command No one likes to vomit V(x) === ____x likes to vomit ∀ x . ! V(x) ! ∃ x . V(x) M(x, y) person ____x enjoys movie ___y There must be some movie everyone enjoys ∃ y . (∀ x . M(x, y)) Everyone has some movie they enjoy ∀ x . (∃ y . M(x, y)) There must be someone who has some movie they enjoy ∃ p . (∃ m . M(p, m)) There must be some movie that some enjoys ∃ m . (∃ p . M(p, m)) Everyone likes every movie ∀ p . (∀ m . M(p, m)) Every movie is liked by everyone ∀ m . (∀ p . M(p, m)) list2 = sort(list1) ∀ list1 that are lists, list2 is a list and list2 contains the same elements as list1 and list2 is "sorted" ∀ index between 0 and length - 2, list2[index] <= list2[index+1] S(l,i) === l[i] <= l[i+1] and if list1 had any element more than once, so does list2