Select the most suitable statement.

Concept

A statement of the form “Every A is B” means that the set A is contained in the set B. A statement of the form “No A is B” means that the two sets have no common member.

In inclusive geometric definitions, a more specialised figure can belong to a broader family when it satisfies all defining properties of that family.

Application

1. A circle is an ellipse whose two semi-axes are equal; equivalently, its eccentricity is 0. Therefore “Every circle is an ellipse” holds under the standard inclusive definition.

2. A circle is an ellipse with eccentricity 0, whereas a hyperbola has eccentricity greater than 1. Thus no non-degenerate circle is a hyperbola.

3. A square has four right angles and opposite sides parallel, so it satisfies every defining condition of a rectangle. Therefore every square is a rectangle.

Contrast and cross-check

• “Every circle is an ellipse” is supported by the equal-semi-axis special case.

• “No circle is a hyperbola” follows from the mutually different conic classes and eccentricities.

• “Every square is a rectangle” follows from the inclusive hierarchy of quadrilaterals.

• “None of the above” would require all three substantive statements to fail, which the definition checks rule out.

Result

Three substantive statements hold, so the suitable set-referential choice is “More than one of the above”.