Question

Draw a Venn diagram for \((A \cup B)-C\).

Short answer

A Venn diagram for \((A \cup B) - C\) should include all of the areas in sets A and B, except for the areas that also belong to set C. These spaces are shaded to represent \((A \cup B) - C\).

Step-by-step solution

- Draw Three Intersecting Circles

Begin by drawing three overlapping circles within a rectangle. Label the circles as A, B and C respectively. The rectangle is referred to as the Universal set, and contains all possible elements. The overlapping areas between the circles represent the intersections of the sets.

- Shade \(A \cup B\)

Next, shade the region that represents the union of sets A and B (\(A \cup B\)). This includes all the areas in sets A and B, as well as the intersection between them.

- Identify and Remove Set C

Now identify the area representing set \(C\) that overlaps with your shaded area from step 2. This represents the intersection of \(C\) and \(A \cup B\). To represent \((A \cup B) - C\), you should exclude this overlapping area from your shaded region. The final shaded region now represents \((A \cup B) - C\).