Question

consider the following sets:
which statements are correct? check all that apply.
r = {x | x is the set of rectangles}
t is a subset of p.
p = {x | x is the set of parallelograms}
e is a subset of i.
t = {x | x is the set of triangles}
s is a subset of t.
i = {x | x is the set of isosceles triangles}
i ⊂ e
e = {x | x is the set of equilateral triangles}
t ⊂ e
s = {x | x is the set of scalene triangles}
r ⊂ p

Explanation:

Step1: Recall the definition of subset

A set \(A\) is a subset of set \(B\) (\(A\subseteq B\)) if every element of \(A\) is also an element of \(B\).

Step2: Analyze \(T\subseteq P\)

Triangles (\(T\)) have 3 sides and parallelograms (\(P\)) have 4 sides. So, \(T\) is not a subset of \(P\).

Step3: Analyze \(E\subseteq I\)

An equilateral triangle (\(E\)) has all three sides equal. An isosceles triangle (\(I\)) has at least two sides equal. Since an equilateral triangle satisfies the condition of an isosceles triangle, \(E\subseteq I\).

Step4: Analyze \(S\subseteq T\)

A scalene triangle (\(S\)) is a type of triangle (\(T\)). So, \(S\subseteq T\).

Step5: Analyze \(I\subseteq E\)

An isosceles triangle may not have all three sides equal. So, \(I
subseteq E\).

Step6: Analyze \(T\subseteq E\)

Not all triangles are equilateral. So, \(T
subseteq E\).

Step7: Analyze \(R\subseteq P\)

A rectangle (\(R\)) is a type of parallelogram (\(P\)) (a parallelogram with right - angles). So, \(R\subseteq P\).

Answer:

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