High School

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------------------------------------------------ Find the cardinal number for the following sets:

A = {101, 102, 103, 104, ..., 132}

B = {101, 103, 105, ..., 201}

Answer :

Final answer:

The cardinal number of set A is 32, and for set B, which contains odd numbers from 101 to 201, it is 51.

Explanation:

The question asks to find the cardinal number of two sets A and B. The cardinal number of a set is the number of elements in the set.

For set A = {101, 102, 103, ..., 132}, we can find the cardinal number by subtracting the smallest element from the largest and adding 1: (132 - 101) + 1 = 32. Therefore, the cardinal number of set A is 32.

For set B = {101, 103, 105, ..., 201}, it is an arithmetic sequence with a common difference of 2 (since it contains all odd numbers starting from 101 up to 201). We use the formula for the nth term of an arithmetic sequence: a_n = a_1 + (n - 1)d. For set B, we are looking for n where a_n = 201, a_1 = 101, and d = 2.

Solving for n gives us: 201 = 101 + (n - 1)*2, which simplifies to n = 51. So, the cardinal number of set B is 51.

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