Practice Problems - Sets, Partitions, and Tree Diagrams

Unions, Intersections, Complements - From 1.1

Let U = {u, v, w, x, y, z, 1, 2, 3}
E = {2, y, w, z}, F = {2, 3, u ,y ,z},
and G = {1, 2, 3, w, y}.
Find (E U F) ∩ G’.

Counting Number of Elements in a Set - From 1.3

Let A and B be subsets of a universal set U:
n(U) = 60
n(B) = 25
n(A U B') = 45
Find n(A ∩ B).

Unions and Intersections of Two Sets in Word Problem - From 1.3

There are 50 students at a house party.
35 of them are drinking Jagermeister,
20 of them are drinking Natty Ice,
and 15 of them are drinking both.
Find the number of students drinking neither Jager nor Natty.

Unions and Intersections of Three Sets in Word Problem - From 1.3

There are 30 students surveyed yielding the following data.
20 of them like Captain
8 like Keystone
10 like miller
5 don't like any of these
6 like neither Captain nor Miller
(note some of these six like none of these drinks)
0 like both Keystone and Miller
How many students surveyed like Captain and exactly one of the two types of beer?

Shading in Venn Diagram - from 1.3

Consider the following Venn Diagram for sets A, B, C. Shown in this diagram are the number of elements in each indicated subset. How many elements are in the set (C’ ∩ B) U A?

venn diagram

Multiplication Principle - from 1.4

A car manufacturer offers sedan and SUV for sale. For the sedan, there are 3 colors available, 4 models available, and an option for sunroof. The SUV only comes in one color, also has 4 models available and an option for sunroof. How many different types of car are available?

Tree Diagram Basics - from 1.4

A coin is flipped once. If the result is a head, the coin is flipped three more times and the result (Head or Tail) of each successive flip is noted. If the result is a tail, the coin is flipped three more times and the number of heads in the three flips is counted. How many outcomes are in the sample space of this experiment?