Maths-

General

Easy

Question

# Find a counterexample to show that the following conjecture is false.

Conjecture: The square of any integer is always greater than the integer.

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 number is the integer “1”.

### The square of any number is always greater than the number. If we take 2, 4 and 6. Their square will be 4, 16 and 36 and they are greater than the integer.

But if take 1. Its square is 1 and it is equal to the integer. So the given conjecture is wrong because it says that the square of any integer is always greater than the integer but in the case of 1 it is equal to 1.

Final Answer:

Hence, the counterexample for the given number is the integer “1”.

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