To determine which of the given sets is not finite, we need to analyze each set individually.
1. First Set: {x | x is a natural number less than 10}
- Natural numbers are the set of positive integers starting from 1.
- Therefore, this set contains: {1, 2, 3, 4, 5, 6, 7, 8, 9}
- There are 9 elements in this set, which is a finite number.
2. Second Set: {x | x is an integer that is less than 0}
- Integers less than 0 are negative integers.
- This set includes all negative integers: {..., -4, -3, -2, -1}
- This set continues indefinitely and has no end.
- Therefore, this set is infinite.
3. Third Set: {x | x is a whole number between 0 and 10}
- Whole numbers are non-negative integers, starting from 0.
- This set includes the numbers: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
- There are 11 elements in this set, which is a finite number.
Upon examining these sets, we find:
- The first set has 9 elements and is finite.
- The second set continues indefinitely with negative integers and is infinite.
- The third set has 11 elements and is finite.
Hence, the set which is not finite is:
O{xlx is an integer that is less than 0}
