Question

for each given set, determine if the set is finite or infinite. if finite, give the cardinality.
set | is the set finite or infinite?
(a) {30, 31, 32, …} | ∘ finite
cardinality:
∘ infinite
(b) {d, e, f, h, v, w, z} | ∘ finite
cardinality:
∘ infinite
(c) the set of odd numbers in {16, 18, 20} | ∘ finite
cardinality:
∘ infinite

Explanation:

Step1: Analyze set (a)

The set $\{30, 31, 32, ...\}$ continues indefinitely with positive integers increasing by 1, so it has no end.

Step2: Analyze set (b)

Count distinct elements: $\{d, e, f, h, v, w, z\}$ has 7 unique elements, so it is finite with cardinality 7.

Step3: Analyze set (c)

The set $\{16, 18, 20\}$ contains only even numbers; there are no odd numbers, so the subset of odd numbers is empty, with cardinality 0.

Answer:

(a) infinite
(b) finite, cardinality: 7
(c) finite, cardinality: 0