Question

11vacr v, algebra 1 sem a cr- a pplications of probability and geometry which sets can be represented using the venn diagram? a is the set of all animals. b is the set of all mammals. a is the set of all polygons. b is the set of all circles. a is the set of all states in the us. b is the set of all world countries. a is the set of all plays by shakespeare. b is the set of all playwrights.

Explanation:

Step1: Analyze the Venn diagram structure

The Venn diagram shows that set \( B \) is entirely contained within set \( A \) (i.e., \( B \subseteq A \)). So we need to find the pair of sets where one set is a subset of the other.

Step2: Evaluate each option

• Option 1: \( A \) (all animals) and \( B \) (all mammals). Mammals are a type of animal, so \( B \subseteq A \). This fits the Venn diagram structure.
• Option 2: \( A \) (all polygons) and \( B \) (all circles). A circle is not a polygon (polygons have straight sides), so \( B \) is not a subset of \( A \). Eliminate this.
• Option 3: \( A \) (all US states) and \( B \) (all world countries). US states are not countries, and countries are not a subset of states. Eliminate this.
• Option 4: \( A \) (all Shakespeare plays) and \( B \) (all playwrights). Plays are not playwrights, and playwrights are not a subset of plays. Eliminate this.

Answer:

A. A is the set of all animals. B is the set of all mammals.