Section 2.2 Subsets and Order of Operation
Determine whether ⊂, ⊆, both or neither can be placed in the blank to make the statement true. {2 comma 6 comma 10 comma 14 comma 18} ___ {14 comma 6 comma 10 comma 18 comma 2}
only ⊆
Intersection
symbol: A ∩ B meaning Intersection: in both A and B example: C ∩ D = {3,4} SHORT LIST ELEMENTS IN "BOTH" SETS
Find the set A ∪ B. U = {1,2,3,4,5,6} A = {1,3,4,5} B = {2,3,6}
A ∪ B = {1,2,3,4,5,6}
Let U = { 1, 2, 3,...}, A = { 1, 2, 3,... , 35}. Use the roster method to write the set A'.
A' = {36,37,38,...}
Let U = {e, f, g, h, i, j, k} and A = {e, h, i, k}. Use the roster method to write the set A'.
A' = {f,g,j}
Find set A' ∩ B' U = {1,2,3,4,5,6,7} A = {1,2,3,4} B = {3,4,5}
A' ∩ B' = {6,7}
Finding number of subset of set A formula
2 ^ n(A)
Select ⊂ or is ⊄ for the blank so that the resulting statement is true. { 12, 10, 4 } ___ { 1, 2, ..., 12 }
⊂ is a subset because {12, 10, 4} are subsets of {1, 2, ..., 12}
Write ⊂ or is ⊄ in each blank so that the resulting statement is true. {x|x is a dog}________{x|x is a black dog}
⊄
Fill in the blank so that the resulting statement is true. The number of subsets of a set with n elements is __________.
2 ^ n
Finding number of proper subset
2 ^ n(A) - 1 subtracts a whole set/number from the subset answer
Find the set A ∩ B. U = {1,2,3,4,5,6} A = {1,2,3,4} B = {1,2,6}
A ∩ B = {1,2}
Complement of a Set formula
A1 = { x | x ∉ A} a1 = all elements in U, but not A A1 = Universal set - A set
Let U = {9,7,2,12,11,10,4,22} A = {9,4,22} C = {7,2,12,11,10} Find A U C'.
C' = U - C C' = {9,4,22} A U C' = {9,4,22}
Fill in the blank so that the resulting statement is true. Set A is a proper subset of set B, expressed as _________, means that set A is a subset of set B and __________.
1. A ⊂ B 2. sets A and B are not equal. Set A is a proper subset of set B, expressed as A ⊂ B, means that set A is a subset of set B and sets A and B are not equal.
Find the set (A U B)' U=1,2,3,4,5,6,7} A = {2,4,6,7} B = 1,4,7}
Find the compliments of set A and B. A' = {1,3,5} B' = {2,3,5,6} (A U B)' - means find the complement first then find the union "long list in both sets". (A U B)' = {3,5}
Proper subset of a Set
Proper Subset: A has some elements of B A ⊂ B A is NOT allowed to equal B example: {3,5} ⊂ D
Subset of a Set
Subset: A has some (or all) elements of B A ⊆ B A is allowed to equal B example: {3,4,5} ⊆ D
Let the set A ∩ Ø. U = {1,2,3,4,5,6,7,8,9,10} A = {2,3,5,8}
The intersection of sets A and the empty set empty set, Ø, A ∩ Ø, is the set of elements common to both set A and set B. There are no elements in empty set. This means that there can be no elements belonging to both A and empty set. Therefore, A intersect empty set equals empty set. b. A ∩ Ø is the empty set.
For the given set, first calculate the number of subsets for the set, then calculate the number of proper subsets. { 1, 9, 14, 6 }
The number of subsets is 16. The number of proper subsets is 15.
Find the set A U Ø. U = {1,2,3,4,5,6} A = {2,4,5,6}
When you have any set union-ed to Ø. Ø means EMPTY set, you have set A. The answer is the numbers in set A because of it being union-ed in set A. union means "LONG LIST/JOINED TOGETHER" A u Ø = {2,4,5,6}
Find the set A ∩ U. U = {1,2,3,4,5,6} A = {1,4,5,6}
a. A ∩ U = {1,4,5,6} intersection "∩" means common in BOTH.
Determine whether ⊂ , ⊆ , both, or neither can be placed in the blank to make the statement true. { negative 8, negative 1, negative 2 } ___ { negative 8, negative 1, negative 2, negative 7 }
both ⊂ & ⊆
Union
symbol: A ∪ B meaning: Union: in A or B (or both) example: C ∪ D = {1,2,3,4,5} LONG LIST AND NO REPEATS "JOINED TOGETHER"
Find the set A U U. U = {1,2,3,4,5,6,7,8} A = {3,4,6,8}
union means joined together/long list. Since U is the universal set, every element in A is also an element in U. Therefore, the union of the two sets is all of the elements in U. A u U = {1,2,3,4,5,6,7,8}
The __________ set of all potential elements.
universal