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Find the cardinal number for the given set. A={3,5,7,dots, 31}

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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.

User Udayaditya Barua
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