To determine which option is a counterexample to the given conjecture, we must identify a product of two numbers that is not greater than both numbers.
Let's analyze each option:
A. \( -1 \cdot -23 = 23 \)
- Here, the product 23 is greater than both -1 and -23. So, this is not a counterexample.
B. \( 6 \cdot 12 = 72 \)
- Here, the product 72 is greater than both 6 and 12. So, this is not a counterexample.
C. \( 4 \cdot 9 = 36 \)
- Here, the product 36 is greater than both 4 and 9. So, this is not a counterexample.
D. \( -3 \cdot -7 = 21 \)
- Here, the product 21 is greater than both -3 and -7. So, this is not a counterexample.
None of the provided options show a product that is less than or equal to both numbers involved. Therefore, it appears there may be an issue with the provided options if the intent is to find a valid counterexample based on typical properties of multiplication.
However, the conjecture itself can be challenged. For instance, the product of two numbers less than 1 (but greater than 0) can provide a counterexample not listed here:
For example: \( 0.5 \cdot 0.5 = 0.25 \)
Here, 0.25 is less than both 0.5 and 0.5, so it acts as a counterexample to the conjecture that the product of two numbers will always be greater than both numbers.
Based on the provided options and the conjecture's definition:
No valid counterexample option (A, B, C, D) fits as all their products are greater.
Which is a counterexample to the following conjecture?
The product of two numbers will always be greater than both numbers.
A.
−1•−23=23
B.
6•12=3
C.
4•9=36
D.
−3•−7=21
1 answer