Question

What is the cardinality of each of these sets?

a) Ø
b) {0}
c) {0}
d) {{0, {0}}}
e) {1, 2, 3}
f) {{1}, {2, {3}}}
g) {{1}, {2}, {3}}
h) {{1,2,3}}

Answer 1

The cardinality of each set is determined by the number of elements it contains.

Step-by-step explanation:

The cardinality of each of these sets is:

1. a) The cardinality of the empty set Ø is 0.
2. b) The cardinality of the set {0} is 1.
3. c) The cardinality of the set {0} is 1.
4. d) The cardinality of the set {{0, {0}}} is 1, as it contains only one element.
5. e) The cardinality of the set {1, 2, 3} is 3, as it contains three elements.
6. f) The cardinality of the set {{1}, {2, {3}}} is 2, as it contains two elements.
7. g) The cardinality of the set {{1}, {2}, {3}} is 3, as it contains three elements.
8. h) The cardinality of the set {{1,2,3}} is 1, as it contains only one element.