Set A is a subset of a set B denoted by AcB, if every element of A belongs to B. In symbol,
If A = {1, 2, 3} and B = { 1, 2, 3, 4} then AcB
A side from the difinition, if there is at least one element found in b but not in A, then A is a proper subsets of any given set, the empty set and the set itself.
The following geberalizationsare consequences od the difinition:
a.Every set is a subset of itself, i.e. AcA
b.An empty set is always a subset of every set, i.e. Ø cA.
c.The set { Ø } and { 0 } are not empty, since each contains one element
d.All sets have a proper subset except the emty set
For example, 0 € { 0 }, but Ø €/ {0}. The elements 0 and Ø are two different symbols. the set {Ø} has onw element designated by the symbol Ø, a symbol not considered as an empty set in this particular example
Example:
The empty set A = { } has only one subset, i.e. A.
Answers & Comments
SUBSETS:
Set A is a subset of a set B denoted by AcB, if every element of A belongs to B. In symbol,
If A = {1, 2, 3} and B = { 1, 2, 3, 4} then AcB
A side from the difinition, if there is at least one element found in b but not in A, then A is a proper subsets of any given set, the empty set and the set itself.
The following geberalizations are consequences od the difinition:
a. Every set is a subset of itself, i.e. AcA
b. An empty set is always a subset of every set, i.e. Ø c A.
c.The set { Ø } and { 0 } are not empty, since each contains one element
d. All sets have a proper subset except the emty set
For example, 0 € { 0 }, but Ø €/ {0}. The elements 0 and Ø are two different symbols. the set {Ø} has onw element designated by the symbol Ø, a symbol not considered as an empty set in this particular example
Example:
The empty set A = { } has only one subset, i.e. A.