Solutions Manual For Finite Mathematics 7th Edition By
Stefan Waner; Steven Costenoble
Definition of set - ANSWER: a collection of items/elements.
Definition of elements - ANSWER: the items in a set
Can you list set elements in any order? - ANSWER: Yes
Can you list a set element twice? - ANSWER: No
∈ means - ANSWER: it is an element of the set
∉ means - ANSWER: it is NOT an element of the set
x:x - ANSWER: x such that x
A ∪ B - Definition of a union - ANSWER: x:x ∈ A or x ∈ B or both
A ∩ B - Definition of intersection - ANSWER: x:x ∈ A and x ∈ B
If A ∩ B =∅, - ANSWER: then we can say that A and B are disjoint
Universal Set - ANSWER: written U, is the larger background set of which all other
sets in the problem are subsets
A' - ANSWER: the complement of A
x: x∈U but x∉A
Can the universal set be a subset of the universal set? - ANSWER: Yes
Formula for the number of subsets - ANSWER: 2ⁿ
Definition of an empty set - ANSWER: a set that contains no elements
It is true to say the ∅ ⊂ A but cannot say - ANSWER: ∅ ∈ A
Definition of a partition - ANSWER: any collection of non-empty, mutually disjoint
sets whose union is all of S
Formula for total number of partitions. - ANSWER: (2ⁿ/2) -1
Definition of n(A) - ANSWER: the number of elements in set A
Definition of A X B - ANSWER: A cross B
(x,y): x ∈ A and y ∈ B
, Ex.
A = (1,2,3)
B = (3,4)
(1,3) , (1,4) , (2,3), (2,4) , (3,3) , (3,4)
Formula for number of elements A X B - ANSWER: n(A X B) = n(A) * n(B)
Definition of Compound Cartesian Products - ANSWER: (x,y,z): x∈A and y∈B and
z∈C
Formula for number of elements A X B X C - ANSWER: n(A X B X C) = n(A) * n(B) * n(C)
Does A' ∩ B' = (A ∩ B)' - ANSWER: No
Does A' ∪ B' = (A ∪ B)' - ANSWER: No
Does A' ∩ B' = (A ∪ B)' - ANSWER: Yes
Does A' ∪ B' = (A ∩ B)' - ANSWER: Yes
Formula for two Venn diagrams - ANSWER: n(A∪B) = n(A) + n(B) - n(A∩B)
Universal formula with complements - ANSWER: n(U) = n(A) + n(A')
n(A) = n(U) - n(A')
A ∩ (B ∪ C) does not equal - ANSWER: (A ∩ B) ∪ C
A ∩ (B ∩ C) equals - ANSWER: (A ∩ B) ∩ C
The Venn Diagram Formula - ANSWER: n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) -
n(B∩C) - n(A∩C) + n(A∩B∩C)
To solve most of the problems that include mutiple intersections and unions, need to
use - ANSWER: Venn Diagrams
What is another strategy to solve venn diagram problems besides the large formula?
- ANSWER: Another way to solves these problems is by drawing two venn diagrams
and subtracting what you need like an equation.
n(A∪B∪C) = - ANSWER: n(U) - n(A' ∩ B' ∩ C')
Tree diagrams - ANSWER: this is where you draw a tree of all the possible outcomes
that are available
To solve some sample space problems, the correct thing to do is to start sketching -
ANSWER: a tree and then recognize the pattern
Stefan Waner; Steven Costenoble
Definition of set - ANSWER: a collection of items/elements.
Definition of elements - ANSWER: the items in a set
Can you list set elements in any order? - ANSWER: Yes
Can you list a set element twice? - ANSWER: No
∈ means - ANSWER: it is an element of the set
∉ means - ANSWER: it is NOT an element of the set
x:x - ANSWER: x such that x
A ∪ B - Definition of a union - ANSWER: x:x ∈ A or x ∈ B or both
A ∩ B - Definition of intersection - ANSWER: x:x ∈ A and x ∈ B
If A ∩ B =∅, - ANSWER: then we can say that A and B are disjoint
Universal Set - ANSWER: written U, is the larger background set of which all other
sets in the problem are subsets
A' - ANSWER: the complement of A
x: x∈U but x∉A
Can the universal set be a subset of the universal set? - ANSWER: Yes
Formula for the number of subsets - ANSWER: 2ⁿ
Definition of an empty set - ANSWER: a set that contains no elements
It is true to say the ∅ ⊂ A but cannot say - ANSWER: ∅ ∈ A
Definition of a partition - ANSWER: any collection of non-empty, mutually disjoint
sets whose union is all of S
Formula for total number of partitions. - ANSWER: (2ⁿ/2) -1
Definition of n(A) - ANSWER: the number of elements in set A
Definition of A X B - ANSWER: A cross B
(x,y): x ∈ A and y ∈ B
, Ex.
A = (1,2,3)
B = (3,4)
(1,3) , (1,4) , (2,3), (2,4) , (3,3) , (3,4)
Formula for number of elements A X B - ANSWER: n(A X B) = n(A) * n(B)
Definition of Compound Cartesian Products - ANSWER: (x,y,z): x∈A and y∈B and
z∈C
Formula for number of elements A X B X C - ANSWER: n(A X B X C) = n(A) * n(B) * n(C)
Does A' ∩ B' = (A ∩ B)' - ANSWER: No
Does A' ∪ B' = (A ∪ B)' - ANSWER: No
Does A' ∩ B' = (A ∪ B)' - ANSWER: Yes
Does A' ∪ B' = (A ∩ B)' - ANSWER: Yes
Formula for two Venn diagrams - ANSWER: n(A∪B) = n(A) + n(B) - n(A∩B)
Universal formula with complements - ANSWER: n(U) = n(A) + n(A')
n(A) = n(U) - n(A')
A ∩ (B ∪ C) does not equal - ANSWER: (A ∩ B) ∪ C
A ∩ (B ∩ C) equals - ANSWER: (A ∩ B) ∩ C
The Venn Diagram Formula - ANSWER: n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) -
n(B∩C) - n(A∩C) + n(A∩B∩C)
To solve most of the problems that include mutiple intersections and unions, need to
use - ANSWER: Venn Diagrams
What is another strategy to solve venn diagram problems besides the large formula?
- ANSWER: Another way to solves these problems is by drawing two venn diagrams
and subtracting what you need like an equation.
n(A∪B∪C) = - ANSWER: n(U) - n(A' ∩ B' ∩ C')
Tree diagrams - ANSWER: this is where you draw a tree of all the possible outcomes
that are available
To solve some sample space problems, the correct thing to do is to start sketching -
ANSWER: a tree and then recognize the pattern
