Final answer:
The cardinal number of the set A={3, 5, 7, ..., 31} is 15, indicating that there are 15 elements within this set.
Step-by-step explanation:
The question asks us to find the cardinal number of the set A which consists of the numbers from 3 to 31, with numbers increasing in increments of 2. The set A can be represented as A={3, 5, 7, ..., 31}. To find the cardinal number, we count how many elements are in the set.
To determine the number of terms in this arithmetic sequence, we use the formula:
n = \(\dfrac{{l - a}}{{d}} + 1\)
where n denotes the number of terms, l is the last term, a is the first term, and d is the common difference. For the set A:
- l = 31 (the last term)
- a = 3 (the first term)
- d = 2 (the common difference between terms)
Plugging the values into the formula, we get:
n = \(\dfrac{{31 - 3}}{{2}} + 1\)
n = \(\dfrac{{28}}{{2}} + 1\)
n = 14 + 1
n = 15
Therefore, the cardinal number of set A is 15, which means there are 15 elements in the set.