Question

consider the sets.
a {x|x is a polygon}
b {x|x is a triangle}
which is true?
options: b ⊂ a, a^c = b, a ⊂ b, b^c = a

Explanation:

Step1: Recall Set Subset Definition

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

Step2: Analyze Set Elements

• Set \( A \): All polygons (closed figures with 3 or more sides).
• Set \( B \): All triangles (polygons with 3 sides).

Every triangle (element of \( B \)) is a polygon (element of \( A \)), so \( B \subset A \).

• \( A^c \) (complement of \( A \)) would be non - polygons, not equal to \( B \) (triangles are polygons).
• \( A \subset B \) is false because not all polygons are triangles (e.g., quadrilaterals are in \( A \) but not in \( B \)).
• \( B^c \) (complement of \( B \)) would be non - triangles (like quadrilaterals, pentagons etc.), not equal to \( A \) (since \( A \) includes triangles too).

Answer:

\( \boldsymbol{B \subset A} \) (the first option)