SAT Sets and Venn Diagrams
To successfully solve problems about sets and Venn diagrams on the SAT, you need to know:
- the definitions of elements, sets, and subsets
- the meaning of union and intersection of sets
- how to work with Venn diagrams
Examples
Set \(A = \{2, 3, 5, 8, 9\}\)
Set \(B = \{5, 8, 11\}\)How many elements in set \(A\) are also in set \(B?\)
(A) \(\ \ \) Zero
(B) \(\ \ \) One
(C) \(\ \ \) Two
(D) \(\ \ \) Three
(E) \(\ \ \) Five
Correct Answer: C
Solution:
It is easy to see that two elements that are in set \(A\) are also in set \(B:\) 5 and 8.
Incorrect Choices:
(A) and (B)
These choices are just offered to confuse you.(D)
This is how many elements in \(A\) are not in \(B,\) and also how many elements there are in set \(B.\)(E)
This is how many elements there are in set \(A.\)
Sets \(A, B,\) and \(C\) are shown in the Venn diagram above. Each number indicates the number of elements in that region. How many elements are included in sets \(B\) or \(C\) but are not included in set \(A?\)
(A) \(\ \ 6\)
(B) \(\ \ 7\)
(C) \(\ \ 11\)
(D) \(\ \ 17\)
(E) \(\ \ 26\)
Correct Answer: D
Solution:
As shown in the diagram above, there are 9 elements included in \(B\) only, 2 elements included in \(C\) only, and 6 elements included in both \(B\) and \(C,\) but not in \(A.\) Therefore, there are 9+2+6=17 such elements.
Incorrect Choices:
(A)
This is how many elements are common to both \(B\) and \(C\) that are not also included in \(A.\)(B)
This is how many elements are common to both \(B\) and \(C.\)(C)
This is how many elements are in set \(B\) only or set \(C\) only.(E)
This is how many elements are in \(B\) or in \(C,\) or in both \(B\) and \(C\).
Review
If you thought these examples difficult and you need to review the material, these links will help:
SAT Tips for Sets and Venn Diagrams
- The union of two sets, \(A\) and \(B,\) is that collection of elements that are in \(A,\) or in \(B,\) or in both \(A\) and \(B.\)
- The intersection of two sets, \(A\) and \(B,\) is that collection of elements that are only in both \(A\) and \(B.\)
- If every element in set \(A\) is an element in set \(B,\) then \(A\) is a subset of \(B.\)
- SAT General Tips