Maths-
General
Easy
Question
Show the conjecture is false by finding a counterexample. If the product of two numbers is positive, then the two numbers must both be positive.
Hint:
Inductive Reasoning is the process of drawing a general conclusion by observing a pattern based on the observations and this conclusion is called conjecture.
Counterexample: It is an example which shows that the conjecture is false.
The correct answer is: Hence, the counterexample for the given conjecture is the product of -1 and -3.
Let’s take the pair (2,4), (8,9) and (10,11)
Write the product of the numbers in the given pair
2 × 4 = 8
8 × 9 = 72
10 × 11 = 110
We can see that the product of two positive numbers is positive
But id we take a pair (-1,-3). Their product is
-1 × (-3) = 3
The product of -1 and -3 is positive but the numbers are not positive. So, the given conjecture is wrong
Final Answer:
Hence, the counterexample for the given conjecture is the product of -1 and -3.
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