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General

Easy

Question

# Show the conjecture is false by finding a counterexample.

If the product of two numbers is even, then the two numbers must be even.

## The correct answer is: the given conjecture is false

### We have given a statement

If the product of two numbers is even, then the two numbers must be even.

We have to show the given conjecture is false.

Let us take two even numbers 6 and 8

Product of considered numbers = 6 x 8 = 48

Product we get is an even number , so the given statement is true for considered values.

If we consider one odd and one even number , 5 and 6

Product = 5 x 6 = 30

So, the product obtained is an even which contradicts the given statement

So, We can say that if the product of two numbers is even, then the two numbers need be even.

So, the given conjecture is false.

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