Question

consider the sets below. a {x|x is a polygon} b {x|x is a triangle} which is true? a ⊂ b b ⊂ a aᶜ = b bᶜ = a

Explanation:

Step1: Recall set - inclusion definition

A set $B$ is a subset of a set $A$ (denoted $B\subseteq A$) if every element of $B$ is an element of $A$.

Step2: Analyze the sets

A triangle is a type of polygon. That is, every triangle is a polygon. But not every polygon is a triangle.

Step3: Evaluate each option

• Option 1: $A\subset B$ means every element of $A$ is in $B$. But there are polygons that are not triangles, so this is false.
• Option 2: $B\subset A$ means every element of $B$ (every triangle) is in $A$ (the set of polygons), which is true.
• Option 3: $A^{c}=B$. The complement of $A$ ($A^{c}$) is the set of all non - polygon elements. This is not equal to $B$ (the set of triangles), so this is false.
• Option 4: $B^{c}=A$. The complement of $B$ ($B^{c}$) is the set of all non - triangle elements. This is not equal to $A$ (the set of polygons), so this is false.

Answer:

B $\subset$ A