Question

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}}}

Answer 1

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

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