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

"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.

Hope this helps.

Answer 2

The correct answers are:

B. E is a subset of I.

C. S is a subset of T.

F. R ⊂ P

The statements are correct.

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