CMSC 302 CH 2 Quiz Practice Problems
What is the cardinality of each of these sets: {a} {{a}} {a,{a}} {a,{a},{a,{a}}} {a,{a},{a,{a}},a}
1 1 2 3 3
Find the sets A and B if A − B = {2, 3, 7}, B − A = {5, 8}, and A ∩ B = {1, 4, 6}.
A = {1, 2, 3, 4, 6, 7} B = {1, 4, 5, 6, 8}
Select two sets A and B such that A ∈ B and A ⊆ B
A = {1}, B = {1, {1}}
Let A i = { 1 , 2 , 3 , . . . , i } for i = 1 , 2 , 3 , ... Find ⋃ i = 1 n A i
An
Suppose that A = {a, b, c, d}, B = {c, d}, C = {b, d}, and D = {a, d, f, h}. Determine which of these sets are subsets of which other of these sets. A ⊂ B B ⊂ A A ⊂ C C ⊂ A A ⊂ D
C ⊂ A B ⊂ A
Use a Venn diagram to illustrate the relationships A ⊂ B and B ⊂ C.
Circle C contains circle B and circle B contains circle A
Let A and B be sets. Show that ( A ∪ B ) − ( A ∩ B ) = ( A − B ) ∪ ( B − A ).
Let A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. Since A ∪ B = {1, 2, 3, 4, 6, 8} and A ∩ B = {2, 4}, ( A ∪ B ) − ( A ∩ B ) = {1, 3, 6, 8} ( A − B ) = {1, 3} and ( B − A ) = {6, 8}, ( A − B ) ∪ ( B − A ) = {1, 3, 6, 8}, so the equation is correct.
Is 3 an element of the following sets: {{{3}},{3}} {3,{3}} {{3},{3,{3}}} {{3}}} {x ∈ R | x is an integer greater than 1} {x ∈ R | x is the square of an integer}
No Yes No No Yes No
Use a Venn diagram to show the relationship A ∪ B.
Regular venn diagram with both A and B circles fully shaded
Use a Venn diagram to show the relationship A - B.
Regular venn diagram with just the A circle shaded alone
Use a Venn diagram to show the relationship A ⊃ B.
Should be A circle with B circle inside
Which Venn diagram represents A ∪ ( B − C )
Venn diagram of A,B,C with A completely filled in and B partially
Which Venn diagram represents ( A ∩ B ¯ ) ∪ ( A ∩ C ¯ )?
Venn diagram of A,B,C with A completely shaded except the center
Which Venn diagram represents ( A ∩ B ) ∪ ( A ∩ C )?
Venn diagram of A,B,C with the center shaded and the center of A and C and the center of A and B shaded
What is the cardinality of the following set: ∅
o
True or false: a an element of the set {{a}, a, {a, {a}}}.
true
Let A = {1, 2}, B = {a, b}, and C = {x, y, z}. Find: A x B C x B A x B x C B x B
{(1, a), (1, b), (2, a), (2, b)} {(x, a), (x, b), (y, a), (y, b), (z, a), (z, b)} {(1, a, x), (1, a, y), (1, a, z), (1, b, x), (1, b, y), (1, b, z), (2, a, x), (2, a, y), (2, a, z), (2, b, x), (2, b, y), (2, b, z)} {(a, a), (a, b), (b, a), (b, b)}
Let Let A = {3, 4}, B = {10, 15}, and C = {x, y, z}. Find: B × A
{(10, 3), (10, 4), (15, 3), (15, 4)}
Let Let A = {3, 4}, B = {10, 15}, and C = {x, y, z}. Find: A × B
{(3, 10), (3, 15), (4, 10), (4, 15)}
Let Let A = {3, 4}, B = {10, 15}, and C = {x, y, z}. Find: A × B × C
{(3, 10, x), (3, 10, y), (3, 10, z), (3, 15, x), (3, 15, y), (3, 15, z), (4, 10, x), (4, 10, y), (4, 10, z), (4, 15, x), (4, 15, y), (4, 15, z)}
Let Let A = {3, 4}, B = {10, 15}, and C = {x, y, z}. Find: A × A
{(3, 3), (3, 4), (4, 3), (4, 4)}
List the elements of the following sets: {x | x is a real number such that x2 = 1} {-1, 1} {x | x is a positive integer less than 12} {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} {x | x is the square of an integer and x < 100} {x | x is an integer such that x2 = 2}
{-1, 1} {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} ∅
Let = {0, 1,...,i}. Find: ⋃(n)(j=1)= Ai
{0, 1, 2, ..., n}
Let A = {1, 2, 3, 4, 5} and B = {0, 3, 6}. Find: A ∪ B A ∩ B A - B B - A
{0, 1, 2, 3, 4, 5, 6} {3} {1, 2, 4, 5} {0,6}
Let = {0, 1,...,i}. Find: ⋂(N)(i =1)= Ai
{0,1}
Match the set builder notation to the listing of the elements. {x | x is a multiple of 2 and 0 <= x <= 12} {x | x is a positive and x <= 12} {x | x <= 1 or x >= 12} {x | x % 2 == 0 or x % 3 = 0} {x | x % 2 == 0 and x % 3 = 0}
{0,2,4,6,8,10,12} {1,2,3,4,5,6,7,8,9,10,11,12} {....,-2,-1,0,1,12,13,14,15..} {-6,-3,-2,0,2,3,4,6...} {..,-6,06,..}
Let U = {1, 2, 3, ..., 19, 20} be the universal set and A = {1, 2, 3, 4, 5} and B = {7, 3, 1, 5, 6, 2, 4, 8}. Find: A ∪ B
{1, 2, 3, 4, 5, 6, 7, 8}
Let U = {1, 2, 3, ..., 19, 20} be the universal set and A = {1, 2, 3, 4, 5} and B = {7, 3, 1, 5, 6, 2, 4, 8}. Find: B − A (line over top)
{1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}
Let U = {1, 2, 3, ..., 19, 20} be the universal set and A = {1, 2, 3, 4, 5} and B = {7, 3, 1, 5, 6, 2, 4, 8}. Find: A ∩ B
{1, 2, 3, 4, 5}
Using A = {1, 2, 3}, select the set(s) B where: A c B
{1, 2, 3, 4}
Using A = {1, 2, 3}, select the set(s) B where: A __c__ B
{1, 2, 3, 4} {1, 2, 3}
List the elements of the following sets: Z = {x | x = y2 for y > 0} {0, 1, 4, 9, 16, 25, ...}
{1, 4, 9, 16, 25, ...}
List the elements of the following sets: Z = {x | x is an odd number from 15 to 35, inclusive} {17, 19, 21, 23, 25, 27, 29, 31, 33}
{15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35}
Let A i = { 1 , 2 , 3 , . . . , i } for i = 1 , 2 , 3 , ... Find ⋂ i = 1 n A i.
{1}
Let A - B = {2}, B - A = {6, 9, 3, 8} and A ∩ B = {7}. Find sets A and B. A {2, 7} B {7}
{2, 7} {3, 6, 7, 8, 9}
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find: A ∩ B ∩ C A ∪ B ∪ C (A ∪ B) ∩ C (A ∩ B) ∪ C
{4,6} {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} {4, 5, 6, 8, 10} {0, 2, 4, 5, 6, 7, 8, 9, 10}
Find the power set of each of the sets below. To get the correct answer start small and go in order. {1,2} {{1,2}, 1} {1, 2, 3} {1}
{∅, {1}, {2}, {1, 2}} {∅, {{1, 2}}, {1}, {{1, 2}, 1}} {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}} {∅, {1}}
List the power set of each of the following set: P({x, y, z}) {x, y, z}
{∅, {x}, {y}, {z}, {x, y}, {x, z}, {y, z}, {xyz}}
List the power set of each of the following set: P(∅) ∅
{∅}
Let U = {1, 2, 3, ..., 19, 20} be the universal set and A = {1, 2, 3, 4, 5} and B = {7, 3, 1, 5, 6, 2, 4, 8}. Find: A − B
∅
What is the cardinality of the following set: P({b,b,{b,b}})
2
Let S = {3, 4, 7, 5, 2}. Find: ∑ x ∈ s x ∏ x ∈ s x m i n x ∈ s x m a x x ∈ s x
21 840 2 7
What is the cardinality of the following set: {b,{b},{b,{b}}}
3
What is the cardinality of the following set: {a, b, d, b, c}
4
Answer true or false to the following statements: ∅ ∈ {0} ∅ ⊂ {0} {∅} ⊆ {∅} 0 ∈ ∅ {0} ⊂ ∅ {0} ∈ {0} {0} ⊂ {0} {∅} ⊆ {∅} {∅} ⊇ {∅}
false true true false false false false true true
List the power set of each of the following set: P({3}) {3}
{∅, {3}}
