- A Venn diagram is a way to picture sets.
- Draw a box to represent the Universial set.
- Label it, in the upper left corner with a U.
- Inside the box, draw cricles to represent subsets
- Label each with the corresponding set letter.
- There is one way to draw a Venn diagram of one set.
- There are four ways to draw a Venn diagram of two sets.
- Use the most generic
- Draw a Venn diagram representing the sets
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
- The generic way to draw a Venn diagram of three sets.
- Draw a Venn diagram representing the sets
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
C = {a,d,f,h}
- The complement of a set A, symbolized by A', is the set of all elements in the universal set not in the set A.
- Illustrate complement in a Venn diagram
-
U = {a,b,c,...j},
A = {a,c,e,g,i}
Find A'
- The intersection of sets A and B, symbolized by A ∩ B, is the set containing all elements that are common to both sets A and B.
- Alternate: The intersections of sets A and B is the set containing all elements that are in both set A and in set B.
- Illustrate intersection in a Venn diagram
-
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
Find A ∩ B
Find A' ∩ B
Find (A ∩ B)'
- The union of two sets A and B, symbolized by A ∪ B, is the set containing all of the elements that are members of set A, or of set B (or of both)
- Illustrate union in a Venn diagram
-
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
Find A ∪ B
Find A' ∪ B
Find (A ∪ B)'
- And is most often associated with intersection (both must be true)
- Something is in set A and set B.
- Or is most often associated with union.
- Something is in set A or set B.
- This is the inclusive or, one or the other or both.
- n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
-
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
Find n(A ∪ B)
- The difference of two sets A and B, symbolized by A-B, is the set of elements in set A that are not in set B.
-
U = {a,b,c,...j},
A = {a,c,e,g,i}
B = {a,b,c,d}
Find A-B