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

Explanation:

Step1: Analyze \( T \subseteq P \)

Triangles (\( T \)) have 3 sides, parallelograms (\( P \)) have 4 sides. No triangle is a parallelogram, so \( T \) is not a subset of \( P \).

Step2: Analyze \( E \subseteq I \)

Equilateral triangles (\( E \)) have all sides equal, so they are also isosceles (at least two sides equal). Thus, every equilateral triangle is an isosceles triangle, so \( E \subseteq I \) is true.

Step3: Analyze \( S \subseteq T \)

Scalene triangles (\( S \)) have all sides unequal, and they are still triangles. So every scalene triangle is a triangle, so \( S \subseteq T \) is true.

Step4: Analyze \( I \subset E \)

Isosceles triangles (\( I \)) can have only two equal sides, while equilateral (\( E \)) have three. Not all isosceles are equilateral, so \( I
ot\subset E \).

Step5: Analyze \( T \subset E \)

Triangles (\( T \)) include scalene, isosceles (non - equilateral), etc. Not all triangles are equilateral, so \( T
ot\subset E \).

Step6: Analyze \( R \subset P \)

A rectangle has opposite sides parallel and equal (meets parallelogram definition). And there are parallelograms that are not rectangles (e.g., non - right parallelograms). So every rectangle is a parallelogram, so \( R \subset P \) is true.

Answer:

• \( E \) is a subset of \( I \).
• \( S \) is a subset of \( T \).
• \( R \subset P \)