1) Let’s come up with some personalized sets. Think about five people in your social circle; friends, co-workers, relatives, classmates, any five people. Write down a list of these people including yourself as the first person (2) Now for each person make a list of who else they know on the list. For shorthand, list each person as 1, 2, 3, 4, 5, 6 (1 is you and the other five are 2 − 6.) This is actually just a list of subsets of {1, 2, 3, 4, 5, 6}! Each social group is a subset. (3) Do you think a Venn diagram would help you visualize these six social groups? Why or why not?
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For this Big Problem, we’ll combine matrices and sets!
(1) Let’s come up with some personalized sets. Think about five people in your social circle; friends, co-workers, relatives, classmates, any five people. Write down a list of these people including yourself as the first person
(2) Now for each person make a list of who else they know on the list. For shorthand, list each person as 1, 2, 3, 4, 5, 6 (1 is you and the other five are 2 − 6.) This is actually just a list of subsets of {1, 2, 3, 4, 5, 6}! Each social group is a subset.
(3) Do you think a Venn diagram would help you visualize these six social groups? Why or why not?
(4) Instead of drawing a diagram we can use a 6 × 6 matrix: Row 1 will be your social group, Row 2 will be the social group of Person 2, etc. Column 1 will be person 1, Column 2 will be Person 2, etc. Fill in the rows one at a time by putting a 1 if that column is a person in the social group and a 0 otherwise.
(5) What do you notice about Row 1? What do you notice about Column 1? Why do you think that happens?
(6) Try comparing Row 2 and Column 2. What do you notice? Why do you think that happens?
(7) Add up all the numbers in Row 3. Compare it to the size of person 3’s social group. What do you notice? Why do you think that happens?
(8) Do you notice any other interesting things about this matrix? Why do you think that happens?
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