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

Answer 1

To analyze the sets:

- Set A contains all polygons, which includes various types of polygons such as triangles, squares, rectangles, pentagons, etc.
- Set B specifically contains only triangles.

From this information, we can establish the following relationships:

1. **A ⊂ B**: This statement is false. Set A includes more shapes than just triangles (e.g., quadrilaterals), so not all polygons are triangles.

2. **B ⊂ A**: This statement is true. Since all triangles are indeed polygons, the set of triangles (B) is a subset of the set of polygons (A).

3. **Ac = B**: This statement is false. The complement of set A (denoted Ac) would consist of all shapes that are not polygons, and this does not include triangles.

4. **Bc = A**: This statement is false. The complement of set B (denoted Bc) would consist of all polygons that are not triangles, which does not make it equal to the set of all polygons (A).

Therefore, the only true statement is **B ⊂ A**.