Question: Determine whether the given set is finite or infinite. Consider the set N of positive integers to…

Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set. {n∈N| n>75}

Choose the correct answer below. A. The set is infinite because the positive integers starting at 76 can continue increasing until they reach an ending point. B. The set is finite because the positive integers starting at 76 can continue increasing without an end. C. The set is finite because the positive integers starting at 76 can continue increasing until they reach an ending point. D. The set is infinite because the positive integers starting at 76 can continue increasing without an end.

Solution

The problem is asking whether the set \( \{ n \in \mathbb{N} \mid n > 75 \} \) is finite or infinite. Since the set of positive integers greater than 75 is \( \{ 76, 77, 78, \ldots \} \), it continues indefinitely because there is no largest positive integer. Therefore, the set is infinite. The correct answer is: D. The set is infinite because the positive integers starting at 76 can continue increasing without an end.