Question:
Which of the following sets are equal?
A = {x | x^2 − 4x + 3 = 0}, C = {x | x ∈ N, x < 3}, E = {1, 2}, G = {3, 1}, B={x|x^2−3x+ 2 = 0},
D = {x|x∈N, x is odd, x<5}, F={1,2,1}, H={1,1,3}. Hint: for the quadratic Equations, get the values
of x which shall be elements of set A and B.)
2. List the elements of the following sets if the universal set is U = {a, b, c, ..., y, z}.
Furthermore, identify which of the sets, if any, are equal.
A = {x |x is a vowel}, C = {x |x precedes f in the alphabet}, B = {x |x is a letter in the
word “little”}, D = {x |x is a letter in the word “title”}.
3. Let A= {1,2,...,8,9}, B={2,4,6,8}, C={1,3,5,7,9}, D={3,4,5}, E={3,5}. Which of the
these sets can equal a set X under each of the following conditions?
(a) X and B are disjoint. (c) X⊆A but X ⊈ C. (b) X ⊆ D but X ⊈ B. (d) X⊆C but X ⊈ A.
4. Consider the universal set U = {1,2,3,...,8,9} and sets A={1,2,5,6}, B={2,5,7},
C={1,3,5,7,9}. Find: (a) A∩B and A∩C (b) A∪B and B∪C (d)A\BandA\C
(f)(A∪C)\Band(B⊕C)\A
(c)AC and CC (e) A⊕B and A⊕C
5. The formula A\B = A ∩ B C defines the difference operation in terms of the operations
of intersection and complement. Find a formula that defines the union A ∪ B in terms
of the operations of intersection and complement.
6. The Venn diagram in Fig. (a) shows sets A, B, C.
Shade the following sets: (a) A\(B∪C);
(b)AC∩(B∪C); (c)AC∩(C\B). ( Note you can draw
different diagram for each answer to avoid shading overlapping and
congestion.)
7. Write the dual of each equation:
(a) A=(BC∩A)∪(A∩B)
(b) (A∩B)∪(AC∩B)∪(A∩BC)∪(AC∩BC)=U
8. Use the laws in Table 1 - 1 to prove each set identity:
(a) (A∩B)∪(A∩BC) = A
(b) A∪B=(A∩BC)∪(AC∩B)∪(A∩B)
Section Two
9. Determine which of the following sets are finite:
(a) Lines parallel to the x axis. (c) Integers which are multiples of 5.
(b) Letters in the English alphabet. (d) Animals living on the earth.
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10. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted
to see which of three popular options, air-conditioning (A), radio (R), and power
windows (W ), were already installed. The survey found:
15 had air-conditioning (A), 12 had radio (R), 11 had power windows (W), 5 had A and
P , 9 had A and R, 3 had all three options. 4 had R and W,
Find the number of cars that had:(a) only W; (b) only A; (c) only R; (d) R and W but
not A; (e) A and R but not W; (f) only one of the options; (g) at least one option; (h)
none of the options.
11. Find the power set P(A) of A={1,2,3,4,5}.
12. Given A = [{a,b},{c},{d,e,f}]. (a) List the elements of A. (b) Find n(A). (c) Find the
power set of A.
13. Let S = {1, 2, ..., 8, 9}. Determine whether or not each of the following is a partition
of S :
(a) [{1,3,6},{2,8},{5,7,9}]
(b) [{1,5,7},{2,4,8,9},{3,5,6}]
(c) [{2,4,5,8},{1,9},{3,6,7}]
(d) [{1,2,7},{3,5},{4,6,8,9},{3,5}]
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