Question

consider the following sets.
u = {all triangles}
e = {x|x ∈ u and x is equilateral}
i = {x|x ∈ u and x is isosceles}
s = {x|x ∈ u and x is scalene}
a = {x|x ∈ u and x is acute}
o = {x|x ∈ u and x is obtuse}
r = {x|x ∈ u and x is right}
which is a subset of i?
o e
o s
o a
o r

Explanation:

Step1: Recall the definitions

An equilateral triangle has all three sides equal. An isosceles triangle has at least two sides equal. A scalene triangle has no sides equal. An acute triangle has all angles less than \(90^{\circ}\). An obtuse triangle has one angle greater than \(90^{\circ}\). A right triangle has one angle equal to \(90^{\circ}\).

Step2: Analyze the relationship between sets

Since an equilateral triangle (set \(E\)) has all three sides equal, it satisfies the condition of having at least two sides equal (the definition of an isosceles triangle, set \(I\)). So, every element of \(E\) is an element of \(I\).
For set \(S\) (scalene triangles), they have no sides equal, so they are not isosceles. For set \(A\) (acute triangles), an acute triangle may or may not be isosceles. For set \(R\) (right - angled triangles), a right - angled triangle may or may not be isosceles.

Answer:

E. Option Text