What is the cardinality of each of these sets? a) {a, 0, {a, 0}} b) {{a}} c) {∅, a, {a}} d) {0, 1, a, {a}, {a, {a}}}

a)

Three elements: $a, 0, \{a,0\}$

$|\{a,0,\{a,0\}\}|=3$

b)

One element: $\{a\}$

$|\{\{a\}\}|=1$

c)

Three elements: $\empty, a, \{a\}$

$|\{\empty,a,\{a\}\}|=3$

d)

Five elements: $0, 1,a, \{a\},\{a,\{a\}\}$

$|\{0,1,a,\{a\},\{a,\{a\}\}\}|=5$