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Consider the following sets:

[tex]\[ U = \{\text{all triangles}\} \][/tex]

[tex]\[ E = \{x \mid x \in U \text{ and } x \text{ is equilateral}\} \][/tex]

[tex]\[ I = \{x \mid x \in U \text{ and } x \text{ is isosceles}\} \][/tex]

[tex]\[ S = \{x \mid x \in U \text{ and } x \text{ is scalene}\} \][/tex]

[tex]\[ A = \{x \mid x \in U \text{ and } x \text{ is acute}\} \][/tex]

[tex]\[ O = \{x \mid x \in U \text{ and } x \text{ is obtuse}\} \][/tex]

[tex]\[ R = \{x \mid x \in U \text{ and } x \text{ is right}\} \][/tex]

Which is a subset of [tex]\( I \)[/tex]?

A. [tex]\( E \)[/tex]

B. [tex]\( S \)[/tex]

C. [tex]\( A \)[/tex]

D. [tex]\( R \)[/tex]

Sagot :

GinnyAnsweridn
To determine which set is a subset of [tex]\( I \)[/tex], we need to analyze the definitions and properties of each type of triangle in relation to an isosceles triangle.

1. Set [tex]\( E \)[/tex] (Equilateral Triangles):
- An equilateral triangle is a triangle in which all three sides are of equal length.
- Every equilateral triangle is also isosceles (because it has at least two equal sides).
- Therefore, [tex]\( E \subseteq I \)[/tex].

2. Set [tex]\( S \)[/tex] (Scalene Triangles):
- A scalene triangle is a triangle in which all three sides are of different lengths.
- Since none of the sides are equal, a scalene triangle can never be isosceles.
- Therefore, [tex]\( S \nsubseteq I \)[/tex].

3. Set [tex]\( A \)[/tex] (Acute Triangles):
- An acute triangle is a triangle in which all three angles are less than 90 degrees.
- Acute triangles can be scalene, isosceles, or equilateral, so not all acute triangles are isosceles.
- Therefore, [tex]\( A \nsubseteq I \)[/tex].

4. Set [tex]\( R \)[/tex] (Right Triangles):
- A right triangle is a triangle in which one of the angles is exactly 90 degrees.
- Right triangles can be scalene or isosceles, so not all right triangles are isosceles.
- Therefore, [tex]\( R \nsubseteq I \)[/tex].

Based on the above analysis, the set that is a subset of [tex]\( I \)[/tex] (the set of isosceles triangles) is [tex]\( E \)[/tex] (the set of equilateral triangles).

Thus, the subset of [tex]\( I \)[/tex] is:
[tex]\[ \boxed{E} \][/tex]
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