2.1.6. Venn Diagrams

Try these first

1. 1.

   What does a Venn diagram represent?

   Hint

   Think about how sets interact.

2. 2.

   In a Venn diagram, what does the intersection of two sets show?

   Hint

   Look for common areas in the circles.

3. 3.

   What does the union of two sets A and B represent?

   • Only elements in A
   • Only elements in B
   • Elements in A or B or both

   Hint

   Think of it as an inclusive 'or'.

4. 4.

   True or False: The complement of set A includes elements that are not in set A.

   • True
   • False

   Hint

   Recall the definition of complement.

5. 5.

   Three friends are surveyed about their hobbies. Friend A likes reading and swimming, Friend B likes swimming and gaming, and Friend C likes gaming and reading. Represent these hobbies in a Venn diagram and calculate the number of unique hobbies if 2 love swimming.

   Hint

   Identify shared hobbies carefully.

6. 6.

   In a class of 30 students, 12 like math, 18 like science, and 6 like both. How many students like either math or science, and how many don’t like either subject?

   Hint

   Remember to consider overlaps in your calculations.