Answer:
The cardinality of set (a) is 0,
the cardinality of set (b) is 1
and
the cardinality of set (c) is 3.
Step-by-step explanation: We are given to find the cardinality of each of the following sets :
(a) { }.
(b) { { } }.
(c) {a, {a}, {a, {a}} }.
We know that
CARDINALITY of a set is the number of elements present in the set.
(a) The given set is A = { }.
The set A is an empty set, so it does not contain any element. Hence, the cardinality of the set A is 0.
(b) The given set is B = { { } }.
The set is B is singleton set, contains only one element (that is empty set). So, the cardinality of the set B is 1.
(c) The given set is C = {a, {a}, {a, {a}} }.
The set C has three elements, a, the set {a} and the set {a, {a}}. So, the the cardinality of set C is 3.
Thus,
the cardinality of set (a) is 0,
the cardinality of set (b) is 1
and
the cardinality of set (c) is 3.
