Question

for each given set, determine if the set is finite or infinite. if finite, give the cardinality.
(a) {4, 8, 12, 16, …}
is the set finite or infinite?
○ finite
cardinality:
○ infinite
(b) the set of integers greater than 7
is the set finite or infinite?
○ finite
cardinality:
○ infinite
(c) {11, 14, 16, 18}
is the set finite or infinite?
○ finite
cardinality:
○ infinite

Explanation:

Step1: Analyze set (a)

The set $\{4, 8, 12, 16, ...\}$ is an infinite sequence of multiples of 4 that continues indefinitely, so it is infinite.

Step2: Analyze set (b)

Integers greater than 7 are $8,9,10,...$, which go on forever, so the set is infinite.

Step3: Count elements in set (c)

The set $\{11, 14, 16, 18\}$ has 4 distinct, countable elements, so it is finite with cardinality 4.

Answer:

(a) infinite
(b) infinite
(c) finite, cardinality: 4