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mathematics
survey of mathematics

Questions and Answers of Survey of Mathematics

If the statement is true for all sets A and B, write “true.” If it is not true for all sets A and B, write “false.” Assume that A ≠ ϕ, U≠ ϕ, and A ⊂ U.ϕ ⊂ A
Use the Venn diagram in Fig. to list the set of elements in roster form.A (2 4 10 11
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.(B ˆ© C)' 12 10 4 6 \14 6. 11 2 13
Construct a Venn diagram to determine whether the following statements are true for all sets A, B, and C.(A ∪ B') ∪ (A ∪ B) = A ∪ (B ∩ C)'
If the statement is true for all sets A and B, write “true.” If it is not true for all sets A and B, write “false.” Assume that A ≠ ϕ, U≠ ϕ, and A ⊂ U.A ⊂ A
Use the Venn diagram in Fig. to list the set of elements in roster form.A - B' в ртz ве
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.A ˆ© C 12 10 4 6 \14 6. 11 2 13
Construct a Venn diagram to determine whether the following statements are true for all sets A, B, and C.(A' ∪ B') = A ∩ B
If the statement is true for all sets A and B, write “true.” If it is not true for all sets A and B, write “false.” Assume that A ≠ ϕ, U≠ ϕ, and A ⊂ U.A ⊆ A
Use the Venn diagram in Fig. to list the set of elements in roster form.A - B в ртz ве
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.A ˆ© B 12 10 4 6 \14 6. 11 2 13
To determine the sets.A - B' ь і.j ве
If the statement is true for all sets A and B, write “true.” If it is not true for all sets A and B, write “false.” Assume that A ≠ ϕ, U≠ ϕ, and A ⊂ U.If A ⊂ B, then A ⊆ B
Use the Venn diagram in Fig. to list the set of elements in roster form.(A ˆ© B)' в ртz ве
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.B' 12 10 4 6 \14 6. 11 2 13
To determine the sets.(A ˆª B) ˆ© C ь і.j ве
If the statement is true for all sets A and B, write “true.” If it is not true for all sets A and B, write “false.” Assume that A ≠ ϕ, U≠ ϕ, and A ⊂ U.If A ⊆ B, then A ⊂ B
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.C 12 10 4 6 \14 6. 11 2 13
To determine the sets.A ˆ© B ˆ© C ь і.j ве
A set contains nine elements. (a) How many subsets does it have?(b) How many proper subsets does it have?
Use the Venn diagram in Fig. to list the set of elements in roster form.(A ˆª B)' в ртz ве
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.U 12 10 4 6 \14 6. 11 2 13
To determine the sets.A ˆª B ˆª C ь і.j ве
For set A = {a, b, c, d}(a) list all the subsets of set A.(b) state which of the subsets in part (a) are not proper subsets of set A.
Use the Venn diagram in Fig. to list the set of elements in roster form.A ˆª B в ртz ве
Use the Venn diagram in Fig. 2.24 to list the sets in roster form.A 12 10 4 6 \14 6. 11 2 13
To determine the sets.A ˆ© B' ь і.j ве
List all the subsets of the sets givenC = {steak, pork chicken}
Use the Venn diagram in Fig. to list the set of elements in roster form.U в ртz ве
Use Fig. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
To determine the sets.A ˆª C ь і.j ве
List all the subsets of the sets given.B = {cow, horse}
Use the Venn diagram in Fig. to list the set of elements in roster form.A ˆ© B в ртz ве
Use Fig. During a session of the U.S. Senate, three bills were voted on. The votes of six senators are shown. Determine in which region of the figure each senator should be placed. The set labeled
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 3, 6}B = {3, 6, 7}Apply De Morgan’s Law show that (A ∩ B)' = A' ∪ B' for these sets.
Use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible. U B A
Use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible. U A B
Use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible. U A B
letU = {a, b, c, d, e, f, g, h, i, j, k}A = {a, c, d, f, g, i}B = {b, c, d, f, g}C = {a, b, f, i, j}Determine the following.B ∪ C
Use a set statement to write a description of the shaded area. Use union, intersection, and complement as necessary. More than one answer may be possible. U A B
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.(A ∪ B)' ∩ C, (A' ∪ C) ∩ (B' ∪ C)
If A ⊆ B and B ⊆ C,must A ⊂ C?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the followingA' - B'
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.(A ∪ B) ∩ (B ∪ C), B ∪( A ∩ C)
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the following(A - B)'
If A ⊂ B and B ⊆ C,must A ⊂ C?
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.A ∪ (B ∩ C), B ∪ (A ∩ C)
If A ⊂ B and B ⊂ C,must A ⊂ C?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the followingA' ∪ (A ∩ B)
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.A ∪ (B ∪ C), (A ∩ B) ∪ (A ∩ C)
How many elements must a set have if the number of proper subsets of the set is 1/2 of the total number of subsets of the set?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the following(B ∪ A) ∩ ( B' ∪ A')
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.A ∪ (B ∩ C)', A ∩ (B ∪ C)'
A hospital has four members on the board of directors: Arnold, Benitez, Cathy, and Dominique.(a) When the members vote on whether to add a wing to the hospital, how many different ways can they vote
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the following(A ∪ B) ∩ (A ∪ B)'
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.A ∩ (B ∪ C), (B ∪ C) ∩ A
For the set D = {a, b, c}(a) Is a an element of set D?(b) Is c a subset of set D?(c) Is {a, b} a subset of set D?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the following(A ∪ B)' ∩ B
How can you determine whether the set of boys is equivalent to the set of girls at a roller-skating rink?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the followingA' ∩ B'
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the following(A ∪ B)'
Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C.A ∩ (B ∪ C), (A ∩ B) ∪ C
If E ⊆ F and F ⊆ E, what other relationship exists between E and F?
LetU = {1, 2, 3, 4, 5, 6, 7, 8}A = {1, 2, 4, 5, 7}B = {2, 3, 5,}Determine the followingA ∩ B
Use Venn diagrams to determine whether the following statements are equal for all sets A and B.(A' ∩ B), A ∪ B'
Write an expression for the general or nth term, an, for the geometric sequence.5, 25, 125, 625 . . .
Write an expression for the general or nth term, an, for the geometric sequence.3, 12, 48, 192, . . .
State the name of the property illustrated.(24 + 7) + 3 = 24 + (7 + 3)
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).10 and 14
Evaluate the expression.(a) (-5)2(b) -52
Write an expression for the general or nth term, an, for the geometric sequence.2, 1, 1/2, 1/4, . . .
Write an expression for the general or nth term, an, for the geometric sequence.72, 12, 2, 1/3, . . .
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).12 and 21
Perform the indicated operation.4√2 - 9√2
Evaluate the expression.(a) -32(b) (-3)2
Write an expression for the general or nth term, an, for the geometric sequence.-16, -8, -4, -2, . . .
State the name of the property illustrated.√3 • 7 = 7 • √3
Express each terminating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.0.0131
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).15 and 25
Perform the indicated operation.√18 + √50
Evaluate the expression.(a) -24(b) (-2)4
Write an expression for the general or nth term, an, for the geometric sequence.-3, 6, -12, 24, . . .
Simplify the expression. Rationalize the denominator when necessary.√3 • √6
State the name of the property illustrated.3/8 + (1/8 + 3/2) = (3/8 + 1/8) + 3/2
Express each terminating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.0.2345
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).32 and 224
Perform the indicated operation.√20 - √80
Evaluate the expression.(a) (-3)4(b) -34
Simplify the expression. Rationalize the denominator when necessary.√8 • √6
State the name of the property illustrated.-1(x + 4) = (-1) • x + (-1) • 4
Perform the indicated operation without the use of a calculator and express each answer in scientific notation.(200,000) (3600)
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).40 and 900
Perform the indicated operation.4√12 - 7√27
Evaluate the expression.(a) -43(b) (-4)3
State the name of the property illustrated.(r + s) • t = (r • t) + (s • t)
Perform the indicated operation without the use of a calculator and express each answer in scientific notation.(230,000) (3000)
Find (a) The greatest common divisor (GCD) (b) The least common multiple (LCM).120 and 240
Express each repeating decimal number as a quotient of two integers. If possible, reduce the quotient to lowest terms.0.̅8̅
Evaluate the expression.(a) 20161(b)12016
Evaluate the expression using the order of operations.15 − 8 • 2

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