Questions: Find n(A) for the following set. A=104,105,106,107, ..., 150

Transcript text: Find $n(A)$ for the following set. \[ A=\{104,105,106,107, \ldots, 150\} \]

Solution

Solution Steps

To find $ n(A) $, which is the number of elements in the set $ A $, we need to determine the count of integers from 104 to 150 inclusive. This can be done by subtracting the smallest element from the largest element and then adding 1 to include both endpoints.

Step 1: Define the Set

The set $ A $ is defined as follows: \[ A = \{104, 105, 106, \ldots, 150\} \]

Step 2: Identify the Range

The smallest element in the set is $ 104 $ and the largest element is $ 150 $.

Step 3: Calculate the Number of Elements

To find the number of elements $ n(A) $, we use the formula: \[ n(A) = \text{largest element} - \text{smallest element} + 1 \] Substituting the values: \[ n(A) = 150 - 104 + 1 = 47 \]

Final Answer

The number of elements in the set $ A $ is \$\boxed{n(A) = 47}\$.

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