Consider the universe of all polygons with three or four sides, and define the following open statements for this universe.
a(x): all interior angles of x are equal
e(x): x is an equilateral triangle
h(x): all sides of x are equal
i (x): x is an isosceles triangle
p(x): x has an interior angle that exceeds 180°
q(x): x is a quadrilateral
r(x): x is a rectangle
s(x): x is a square
t(x): x is a triangle
Translate each of the following statements into an English sentence, and determine whether the statement is true or false.
(a) ∀x [q(x) ∨ r(x)]
(b) ∀x [i(x) → e(x)]
(c) ∃x [t(x) ∧ p(x)]
(d) ∀x [(a(x) ∧ r(x)) ↔ e(x)]
(e) ∃x [q(x) ∧ → e(x)]
(f) ∃x [r(x) ∧ ¬s(x)]
(g) ∀x [h(x) → e(x)]
(h) ∀x [t(x) → ¬p(x)]
(i) ∀x [s(x) ↔ (a(x) ∧ h(x))]
(j) ∀x [t(x) → (a(x) ↔ h(x))]