Answer to Question #125568 in Discrete Mathematics for kavee

Question

What is the cardinality of each of these sets?
(a)∅
(b){∅}
(c){∅,{∅}}
(d){∅,{∅},{∅,{∅}}}

Answer 1

(a) Cardinality of ∅ is 0.

it is an empty set, hence there are no or 0 elements present.

(b) Cardinality of {∅} is 1.

It contains one element {∅}, that is a set containing an empty set.

(c) Cardinality of {∅,{∅}} is 2.

It contains two elements -- an empty set ( ∅ ) , and a set containing an empty set ( {∅} ).

(d) Cardinality of {∅,{∅},{∅,{∅}}} is 3.

It contains three elements -- an empty set ( ∅ ) , a set containing an empty set ( {∅} ) , and a

set containing {∅,{∅}}. In the third element, the full set {∅,{∅}} is considered as one

element.

For example, a set S = {a , b , {c , d , e} } has a cardinality of 3 . Here, first element is a , second

element is b , and third element is a set {c , d , e }.