Answer
a) 1
b) 1
c) 2
d) 3
Work Step by Step
a) The set {a} contains exactly one element, namely a. So the cardinality of {a} is 1.
b) The set {{a}} contains exactly one element, namely {a}. Thus the cardinality of {{a}} is 1.
c) The set {a,{a}} contains two elements, which are a and {a}. So the cardinality of this set is 2.
d) The set {a, {a}, {a,{a}}} contains the three elements a, {a}, and {a,{a}}. So the cardinality of this set is 3.