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?
○ e
○ s
○ a
○ r

Explanation:

Step1: Define subset condition

A set $X$ is a subset of $I$ if every element of $X$ is an element of $I$.

Step2: Analyze set $I$

$I$ = {all isosceles triangles} (triangles with at least 2 equal sides).

Step3: Analyze option E

$E$ = {all equilateral triangles}. Every equilateral triangle has 3 equal sides, so it satisfies the definition of an isosceles triangle (has at least 2 equal sides). Thus, every element of $E$ is in $I$.

Step4: Eliminate other options

• $S$: Scalene triangles have no equal sides, so not in $I$.
• $A$: Acute triangles can be scalene, so not all are in $I$.
• $R$: Right triangles can be scalene, so not all are in $I$.

Answer:

E