How many elements does each of these sets have where a and b are distinct elements?

a. p ({a, b,{a, b}})

b. p ({?, a,{a},{{a}}})

a) 8

b) 16

Step-by-step explanation:

a) We note that the first set contains three elements: a, b, and {a, b}.

The power set of {a, b, {a, b}} contains all possible elements of {a, b, {a, b}}.

For each element, we have 2 options: the element is either in the subset or the element is not in the subsets. The number of possible subsets is then equal to product the of the number of options for each element.

P ({a, b,{a, b}}) = 2 * 2 * 2 = 2 ^ 3 = 8

b) We note that the second set contains four elements:?, a, {a} and {{a}}.

The power set of {?, a, {a}, {{a}}} contains all possible elements of {?, a, {a}, {{a}}}.

For each element, we have 2 options: the element is either in the subset or the element is not in the subsets. The number of possible subsets is then equal to product the of the number of options for each element.

P ({?, a, {a}, {{a}}}) = 2 * 2 * 2 * 2 = 2 ^ 4 = 16