Question

Consider the following sets:


R = {x | x is the set of rectangles}

P = {x | x is the set of parallelograms}

T = {x | x is the set of triangles}

I = {x | x is the set of isosceles triangles}

E = {x | x is the set of equilateral triangles}

S = {x | x is the set of scalene triangles}

Which statements are correct? Check all that apply.

T is a subset of P.
E is a subset of I.
S is a subset of T.
I ⊂ E
T ⊂ E
R ⊂ P

Answer 1

Correct:
- E is a subset of I. (Every equilateral triangle has at least two equal sides, so it is isosceles. Note: this depends on the convention; if "isosceles" means "exactly two equal sides" then this would be false.)
- S is a subset of T. (Scalene triangles are triangles.)
- R ⊂ P. (Every rectangle is a parallelogram, and there are parallelograms that are not rectangles, so the inclusion is proper.)

Incorrect: T ⊂ P, I ⊂ E, T ⊂ E.