Section SV.3 – Practice Problems

For problems 1 – 12, create a Venn diagram to illustrate each of the following.

1. [latex]\bar{C}[/latex]

2. [latex]A~\cup~B[/latex]

3. [latex]A~\cap~B[/latex]

4. [latex]A~\cap~\bar{B}[/latex]

5. [latex]A~\cup~B~\cup~C[/latex]

6. [latex]A~\cap~B~\cap~C[/latex]

7. [latex](A~\cup~B)~\cap~C[/latex]

8. [latex](C~\cap~B)~\cup~A[/latex]

9. [latex](C~\cap~\bar{A})~\cup~B[/latex]

10. [latex](A~\cup~\bar{B})~\cap~C[/latex]

11. [latex](\bar{A}~\cap~\bar{B})~\cap~C[/latex]

12. [latex](A~\cap~B)~\cup~(A~\cap~\bar{C})[/latex]

13. Draw a Venn Diagram to represent the sets U = {q, w, e, r, t, y, u}, A = {w, e, u}, and B = {r, t, e, u}.

14. Draw a Venn Diagram to represent the sets U = {a, b, c, d, e, f, g, h, i, j, k}, A = {a, b, h, i, j}, B = {c, d, f, i, j}, and C = {f, g, h, j}.

15. Draw a Venn Diagram to represent the sets U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {4, 5, 6, 8}, B = {1, 2, 4, 5, 6, 7}, and C = {3, 4, 7}

For problems 16 – 19, write an expression for the shaded region. There may be more than one way to write an expression for each of the shaded regions.

16.

17.

18.

19.

20. Use the Venn diagram to write each of the sets below in roster form.

a. [latex]\bar{A}~\cap~B[/latex]

b. [latex]\bar{B}~\cup~A[/latex]

21. Use the Venn diagram to write each of the sets below in roster form.

a. [latex]\cup[/latex] (the universal set)

b. [latex]A[/latex]

c. [latex]A~\cap~C[/latex]

d. [latex]B~\cup~C[/latex]

e. [latex]\overline{(A~\cup~B)}[/latex]

f. [latex](A~\cap~B)~\cap~\bar{C}[/latex]

g. [latex]\overline{(A~\cup~C)}~\cap~B[/latex]

h. [latex](\bar{B}~\cap~\bar{C})~\cup~\overline{(B~\cup~A)}[/latex]

22. Use the Venn diagram to write each of the sets below in roster form.

a. [latex]\cup[/latex] (the universal set)

b. [latex]B[/latex]

c. [latex]B~\cap~C[/latex]

d. [latex]A~\cup~C[/latex]

e. [latex]\overline{(B~\cup~C)}[/latex]

f. [latex]A~\cap~B~\cap~\bar{C}[/latex]

g. [latex]\overline{A~\cup~B}~\cap~C[/latex]