Every singleton set has no proper subset. For example {6} has one and only one subset {6}which is improper subset.
Null set or empty set { } has no proper subset.
Write down the proper subset.
| Given that | Two proper subset | possible subset |
| {a,b,c} | {a }, {b} | 2³ = 8 |
| {0,1} | {0},{1} | 2²=4 |
| N = natural number | {1,2},{3,4,5} | infinite∴N={1,2,3…} |
| R = real number | { },{4,5} | Infinite∴R = Q U Q’ |
| {x/x ∈ Q∧ o<x ≤2} | {1}, {2} | Infinite |
(1) Difference Between {a,b} and {{a,b}} ?
Solution:
{a,b} is a set which has two element a and b, where as {{a,b}} is a singleton set whose element {a, b}.
(2) Set {a,b}={b,a} is true or false:
{a,b}={b,a}
is a true set
because arrangement of element in set does not matter
(3) Φ ⊆ {{a}}
True set
because empty set is a subset of every set.
singleton set has proper subset
(4) {a} ⊇ {{a}}
False
As {{a}} is a singleton set having element {a}
But {a} is not a super set of {{a}}
(5) {a} ∈ {{a}}
TRUE
As {{a}} is a singleton set having element {a}
(6) a ∈ {{a}}
FALSE
As {{a}} is a singleton set having element {a}. But a ∈ {a}.
(7) φ ∈ {{a}}
FALSE
As {{a}} is a singleton set having element {a}. But φ ⊆ {{a}}