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
Accepted Solution
A:
"T is a subset of P"
Not true since triangle has three sides but parallelogram has four sides.
"E is a subset of I"
True since equilateral triangles are isosceles triangles with all angles equal.
"S is a subset of T"
True since scalene triangles are still triangle.
"I ⊂ E"
False since there are isosceles triangles those are not equilateral triangles. Namely triangle with angles 20°, 20°, 140°
"T ⊂ E"
False since not all triangles are equilateral. Scalene triangle is one of counterexamples.
"R ⊂ P"
True since rectangles are parallelograms with right angles.
Final answer: E is a subset of I, S is a subset of T, and R ⊂ P.