To determine a counterexample to the conjecture "The difference of two numbers is less than at least one of the numbers," we need to find an example where the difference is not less than at least one of the numbers.
Let's analyze each given example:
1. \( 8 - 1 = 7 \)
- Here, 7 is less than 8 but not less than 1. The conjecture holds because 7 is less than at least one of the numbers (8).
2. \( 12 - 7 = 5 \)
- Here, 5 is less than 12 but not less than 7. The conjecture holds because 5 is less than at least one of the numbers (12).
3. \( (-3) - 5 = -8 \)
- Here, -8 is less than both -3 and 5. The conjecture holds because -8 is less than at least one of the numbers (5).
4. \( (-4) - (-9) = 5 \)
- Here, 5 is not less than -4, and it equals 5 (not less than -9). In this case, the conjecture does not hold because 5 is not less than either of the numbers (-4 or -9).
Therefore, the counterexample to the conjecture is:
\[ (-4) - (-9) = 5 \]
This is the correct counterexample because the difference (5) is not less than either of the original numbers (-4 or -9).
3.
Which is a counterexample to the following conjecture?
The difference of two numbers is less than at least one of the numbers.
8 – 1 = 7
12 – 7 = 5
(–3) – 5 = –8
(–4) – (–9) = 5
1 answer
3 answers