DESCRIPTION OF INTERACTIVE

This interactive is not suitable for screen readers.

Take a screen capture of your created venn diagram. Record your reflections on the following questions:

  1. Do all of the elements on the diagram add to 50?
  2. Did it take you several tries to figure it out?
  3. What are the challenges associated with this question?
  4. What is your strategy to solve the problem?
 

The Union of Sets

We also use the notation  A U B as the “Union” of the two sets, everything in both sets combined.  

This is an image of a Venn Diagram, two black circles with an overlapping section everything inside the circles is coloured red.

For the example of the flu symptoms, it is patients with headache “OR” a cold.  It includes people with just a headache, just a cold, and both headache and cold.  

This is an image of a Venn Diagram, two black circles with an overlapping section everything outside the circles is coloured red.

We also use the complement.  If we wanted to say people in neither A nor B, we would say it as people in the complement of the union of A or B, or A U B apostrophe. 

In the example A U B apostrophe was given in the question, it was the 12 people that have neither a cold nor a headache.  

Probability and Counting Intersections and Unions

We can count each of these sets or represent the probability of each of these sets by using our function notation and n and P.

Refer to the table for a summary:

Symbol Meaning
n(A) or n(B) Number of elements in A or B
P(A) or P(B) Probability of A or B

n of A upside down U B or P of A upside down U B 

Intersection of sets: Number of elements or Probability of an element being in both A “and” B

n of A U B or P of A U B

Union of sets:  Number of items or Probability of an item being in A “or” B

This is the ePortfolio icon. Example 1

Consider a game involving red cards and number cards. To compare to Einstein’s quote from the Introduction: What is red is not always a number card, and what is a number card is not always red. We know, just as we hope there is popular and right, there are red number cards.

This is an image of each card in a standard deck of cards on a green background. The suits are in rows with the cards in order from Ace to King.

If A is the set of all red cards, and B is the set of all number cards (non face cards, ie. A-10)  and S is all cards.  

Use the Venn Diagram interactive to draw the Venn Diagram, save with a screen capture, then complete the following table.

VennDiagram

DESCRIPTION OF INTERACTIVE

This interactive is not suitable for screen readers.