Question

core algebra i b-cr
consider the sets below.
a {x|x is a polygon}
b {x|x is a triangle}
which is true?
a⊂b
b⊂a
a^c = b
b^c = a

Explanation:

Step1: Define set memberships

Set $A$ = all polygons (closed 2D shapes with straight sides, e.g., triangles, quadrilaterals, pentagons). Set $B$ = all triangles (3-sided polygons).

Step2: Analyze subset relations

A subset $X \subset Y$ means all elements of $X$ are in $Y$. All triangles are polygons, so every element of $B$ is in $A$.

Step3: Evaluate complement options

$A^c$ is non-polygons (not equal to $B$), $B^c$ is non-triangles (not equal to $A$). $A \subset B$ is false because not all polygons are triangles.

Answer:

B. $B \subset A$