Questions: For each given set, determine if the set is finite or infinite. If finite, give the cardinality. (a) The set of integers greater than 2 (b) f, h, j, k, n (c) 30,60,90, ...

For each given set, determine if the set is finite or infinite. If finite, give the cardinality.

(a) The set of integers greater than 2

(b) f, h, j, k, n

(c) 30,60,90, ...

Transcript text: For each given set, determine if the set is finite or infinite. If finite, give the cardinality. (a) The set of integers greater than 2 (b) $\{f, h, j, k, n\}$ (c) $\{30,60,90, \ldots\}$

Solution

Solution Steps

Step 1: Analyze Set (a)

The set described in (a) is "the set of integers greater than 2." This set can be represented as $\{3, 4, 5, \ldots\}$. Since there is no upper limit to the integers greater than 2, this set is infinite.

Step 2: Analyze Set (b)

The set given in (b) is $\{f, h, j, k, n\}$. This is a finite set because it contains a specific number of elements. The cardinality of this set, which is the number of elements in the set, is 5.

Step 3: Analyze Set (c)

The set described in (c) is $\{30, 60, 90, \ldots\}$. This set is an arithmetic sequence with a common difference of 30. Since there is no specified end to this sequence, it is infinite.