Beginning Activity Beginning Activity 2: Working with Venn Diagrams
1.
Draw a Venn diagram for two sets, \(A\) and \(B\text{,}\) with the assumption that \(A\) is a subset of \(B\text{.}\) On this Venn diagram, lightly shade the area corresponding to \(A^c\text{.}\) Then, determine the region on the Venn diagram that corresponds to \(B^c\text{.}\) What appears to be the relationship between \(A^c\) and \(B^c\text{?}\) Explain.
2.
Draw a general Venn diagram for two sets, \(A\) and \(B\text{.}\) First determine the region that corresponds to the set \(A - B\) and then, on the Venn diagram, shade the region corresponding to \(A - (A - B)\) and shade the region corresponding to \(A \cap B\text{.}\) What appears to be the relationship between these two sets? Explain.